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## Kinematics Practice Problems with Answers

The most complete guide on solving kinematics problems for high schools and colleges. By working through these questions, you can undoubtedly master this topic in physics.

These multiple-choice questions on kinematics for AP Physics 1 are also available to review for students enrolled in AP Physics courses.

All kinematics equations are summarized in the following expressions: \begin{gather*} \Delta x=\frac{v_1+v_2}{2}\times \Delta t \\\\ v=v_0+at \\\\ \Delta x=\frac 12 at^2+v_0t \\\\ v^2-v_0^2=2a\Delta x \end{gather*} In the rest of this long article, you will see how to apply these equations in the given problems.

## Kinematics Practice Problems:

Problem (1): A car slows down its motion from 10 m/s to 6 m/s in 2 seconds under constant acceleration. (a) What is its acceleration? (b) How far did the car travel during this time interval?

Solution : This is the simplest kinematics problem, so we put a bit more time to solve it in detail.

Step 1: Because all these problems are in one dimension, draw a directed horizontal axis (like the positive $x$ axis), and put the object on it, so that it moves in the correct direction.

Step 2: Specify the known and wanted information. Here, in the elapsed time interval $2\,{\rm s}$, the initial and final velocities of the car are given as $v_i=10\,{\rm m/s}$ and $v_f=6\,{\rm m/s}$. The wanted quantity is the constant acceleration of the object (car), $a=?$.

Step 3: Apply the kinematics equation that is appropriate for this situation.

(a) In this problem, we want to find the acceleration, given the time, initial, and final velocities so the kinematics equation $v=v_0+at$ is perfect since the only unknown quantity is acceleration $a$. Thus, \begin{gather*} v=v_0+at\\\\ 6=10+a(2) \\\\ 6-10=2a \\\\\Rightarrow \quad a=\frac{6-10}{2}=-2\quad {\rm \frac{m}{s^2}}\end{gather*} Note that because the problem says the acceleration of the motion is constant, we could use the constant acceleration kinematics equations.

The negative indicates the direction of the acceleration, which is here toward the negative $x$ axis.

(b) "How far'' means the distance traveled by car is wanted, denoted by $x$ in the kinematics equations.

Here, the best equation that relates the known and unknown information is $x=\frac 12 at^2+v_0t$ or $v^2-v_0^2=2ax$. We choose the first, so \begin{align*} x&=\frac 12 at^2+v_0t \\\\&=\frac 12 (-2)(2)^2+(10)(2) \\\\&=16\quad {\rm m}\end{align*}

On the following page you can find over 40+ questions related to applying kinematics equations in velocity and acceleration:

Velocity and acceleration problems

Problem (2): A moving object slows down from $12\,{\rm m/s}$ to rest at a distance of 20 m. Find the acceleration of the object (assumed constant).

Solution : In the diagram below, all known information along with the direction of the uniform motion is shown.

As you can see, one of the common phrases in kinematics problems is "ending or coming to a rest'', which means the final velocity of the object in that time interval (in which we look at the object's motion) is zero, $v_f=0$.

The perfect kinematics equation that solves this problem is $v^2-v_0^2=2a(x-x_0)$ as the only unknown quantity is acceleration $a$.

Keep in mind that in all kinematics equation problems, we can set the initial position of the motion $x_0$ as zero for simplicity, $x_0=0$. \begin{gather*} v^2-v_0^2=2ax\\\\0^2-(12)^2 =2a(20) \\\\ \rightarrow a=\frac{-144}{2\times 20}\\\\\Rightarrow \boxed{a=-3.6\quad {\rm \frac{m}{s^2}}}\end{gather*} As before, the minus sign indicates the direction of the acceleration which is toward the left .

Problem (3): A bullet leaves the muzzle of an 84-cm rifle with a speed of 521 m/s. Find the magnitude of the bullet's acceleration by assuming it is constant inside the barrel of the rifle.

Solution : The bullet accelerates from rest to a speed of 521 m/s at a distance of 0.84 meters. These are our known quantities. The unknown is acceleration $a$. The perfect kinematics equation that relates all these together is $v^2-v_0^2=2a(x-x_0)$, so \begin{gather*}v^2-v_0^2=2a(x-x_0)\\\\ (521)^2-0=2(a)(0.84-0) \\\\ \Rightarrow \boxed{a=1.62\times 10^5\quad {\rm m/s^2}}\end{gather*} A very large acceleration.

Problem (4): A car starts its motion from rest and uniformly accelerates at a rate of $4\,{\rm m/s^2}$ for 2 seconds in a straight line. (a) How far did the car travel during those 2 seconds? (b) What is the car's velocity at the end of that time interval?

Solution : "Start from rest'' means the initial object's velocity is zero, $v_0=0$. The known information are $a=4\,{\rm m/s^2}$, $t=2\,{\rm s}$ and wants the distance traveled $x=?$.

(a) The kinematics equation that relates that information is $x=\frac 12 at^2+v_0 t+x_0$ since the only unknown quantity is $x$ with the given known data above. \begin{align*} x&=\frac 12 at^2+v_0 t+x_0 \\\\&=\frac 12 (4)(2)^2+(0)(2) \\\\&=\boxed{8\quad {\rm m}}\end{align*} As previous, we set $x_0=0$.

(b) Now that the distance traveled by the car in that time interval is known, we can use the following kinematics equation to find the car's final velocity $v$. \begin{align*} v^2-v_0^2 &=2a(x-x_0) \\\\v^2-(0)^2&=2(4)(8-0) \\\\v^2&=64\end{align*} Taking the square root, we get $v$: \[v=\sqrt{64}=\pm 8\quad {\rm \frac ms}\] We know that velocity is a vector quantity in physics and has both a direction and a magnitude.

The magnitude of the velocity (speed) was obtained as 8 m/s, but in what direction? Or we must choose which signs? Because the car is uniformly accelerating without stopping in the positive $x$ axis, the correct sign for velocity is positive.

Therefore, the car's final velocity is $\boxed{v_f=+8\,{\rm m/s}}$.

## Challenging Kinematics Problems

In the following, some challenging kinematics problems are presented, which are for homework.

A driver is moving along at $45\,\rm m/s$ when she suddenly notices a roadblock $100\,\rm m$ ahead. Can the driver stop the vehicle in time to avoid colliding with the obstruction if her reaction time is assumed to be $0.5\,\rm s$ and her car's maximum deceleration is $5\,\rm m/s^2$?

Solution : The time between seeing the obstacle and taking action, such as slamming on the brake, is defined as the reaction time. During this time interval, the moving object travels at a constant speed.

Thus, in all such questions, we have two phases. One is constant speed, and the other is accelerating with negative acceleration (deceleration).

Here, between the time of seeing the barrier and the time of braking, the driver covers a distance of \begin{align*} x_1&=vt_{reac} \\\\ &=25\times 0.5 \\\\ &=12.5\,\rm m\end{align*} In the decelerating phase, the car moves a distance, which is obtained using the following kinematics equation: \begin{gather*} v^2-v_0^2=2ax_2 \\\\ (0)^2-(25)^2=2(-5) x_2 \\\\ \Rightarrow x_2=62.5\,\rm m\end{gather*} Summing these two distances gives a total distance that is a good indication of whether the moving object hits the obstacle or not. \begin{gather*} \Delta x_{actual}=x_1+x_2=75\,\rm m \\\\ \Rightarrow \Delta x_{covered}<\Delta x_{actual} \end{gather*} As a result, because the distance covered by the car is less than the actual distance between the time of seeing the barrier and the obstacle itself, the driver has sufficient time to stop the car in time to avoid a collision.

For a moving car at a constant speed of $90\,\rm km/h$ and a human reaction time of $0.3\,\rm s$; find the stopping distance if it slows down at a rate of $a=3\,\rm m/s^2$.

Solution : We use SI units, so first convert the given speed in these units as below \begin{align*} v&=90\,\rm km/h \\\\ &=\rm 90\times \left(\frac{1000\,m}{3600\,s}\right) \\\\ &=25\,\rm m/s\end{align*} As we said previously, during the reaction time, your car moves at a constant speed and covers a distance of \begin{align*} x_1&=vt_{react} \\\\ &=(25)(0.3) \\\\ &=7.5\,\rm m \end{align*} Deceleration means the moving object slows down, or a decrease per second in the velocity of the car occurs. In this case, we must put the acceleration with a negative sign in the kinematics equations.

During the second phase, your car has negative acceleration and wants to be stopped. Thus, the distance covered during this time interval is found as follows \begin{align*} v^2-v_0^2=2a\Delta x \\\\ (0)^2-(25)^2=2(3)\Delta x \\\\ \Rightarrow \quad \boxed{\Delta x=104.17\,\rm m}\end{align*}

Assume you are traveling $35\,\rm m/s$ when suddenly you see red light traffic $50\,\rm m$ ahead. If it takes you $0.456\,\rm s$ to apply the brakes and the maximum deceleration of the car is $4.5\,\rm m/s^2$, (a) Will you be able to stop the car in time? (b) How far from the time of seeing the red light will you be?

Solution : When you see the red light until you apply the brakes, your car is moving at a constant speed. This time interval is defined as the reaction time, $\Delta t_{react}=0.456\,\rm s$. After you get the brakes on, the car starts to decelerate at a constant rate, $a=-4.5\,\rm m/s^2$. Pay attention to the negative signs of such problems. The negative tells us that the car is decreasing its speed.

(a) In the first phase, the car moves a distance of \begin{align*} x_1&=v\Delta t_{react} \\\\ &=35\times 0.455 \\\\ &=15.96\,\rm m\end{align*} In the phase of deceleration, the car is moving a distance whose magnitude is found using the time-independent kinematics equation as below \begin{gather*} v^2-v_0^2=2ax_2 \\\\ (0)^2-(35)^2=2(4.5)x_2 \\\\ \Rightarrow \quad x_2=136.11\,\rm m\end{gather*} The sum of these two distances traveled gives us the total distance covered by the car from the time of seeing the red traffic light to the moment of a complete stop. \[x_{tot}=x_1+x_2=152.07\,\rm m \] Because the total distance traveled is greater than the actual distance to the red light, the driver will not be able to stop the car in time.

(b) As previously calculated, the total distance traveled by the car is nearly $152\,\rm m$ or the car is about $102\,\rm m$ past the red light traffic.

A person stands on the edge of a $60-\,\rm m$-high cliff and throws two stones vertically downward, $1$ second apart, and sees they both reach the water simultaneously. The first stone had an initial speed of $4\,\rm m/s$. (a) How long after dropping the first stone does the second stone hit the water? (b) How fast was the second stone released? (c) What is the speed of each stone at the instant of hitting the water?

Solution: Because all quantities appearing in the kinematics equation are vectors, we must first choose a positive direction. Here, we take up as a positive $y$ direction.

Both stones arrived in the water at the same time. Thus, calculate the time the first stone was in the air. Next, use the time interval between the two drops to find the duration the second stone was in the air. (a) The first stone is released downward at a speed of $4\,\rm m/s$, thus, its initial velocity is $v_0=-4\,\rm m/s$. The minus sign is for moving in the opposite direction of the chosen direction.

The only relevant kinematics equation that relates this known information is $\Delta y=-\frac 12 gt^2+v_0t$, where $\Delta y=-60\,\rm m$ is the vertical displacement, and the negative indicates that the stone hit a point below the chosen origin. Substituting the numerical values into this and solving for the time duration $t$ gives \begin{gather*} \Delta y=-\frac 12 gt^2+v_0t \\\\ -60=-\frac 12 (10)t^2+(-4)t \\\\ 5t^2+4t-60=0 \\\\ \Rightarrow \boxed{t=3.0\,\rm s} \, , \, t'=-3.8\,\rm s \end{gather*} The second answer is not acceptable.

(b) The second stone was released $1$ second after throwing the first one and arrived at the same time as the first stone. Therefore, the time interval that the second stone was in the air is found to be \begin{align*} t_2&=t_1-1 \\ &=3.0-1\\ &=2\,\rm s\end{align*}

(c) It is better to apply the time-independent kinematics equation $v^2-v_0^2=-2g\Delta y$ to find the stone's velocity at the moment it hit the water. For the first stone, we have \begin{gather*} v^2-v_0^2=-2g\Delta y \\\\ v^2-(-4)^2=-2(10)(-60) \\\\ \Rightarrow \quad \boxed{v=34.8\,\rm m/s} \end{gather*} The second stone's velocity is left to you as an exercise.

In a tennis game, the ball leaves the racket at a speed of $75\,\rm m/s$ whereas it is in contact with the racket for $25\,\rm ms$, and starts at rest. Assume the ball experiences constant acceleration. What was the ball's acceleration during this serve? How far has the ball traveled on this serve?

Solution : In this question, we are asked to find the ball's acceleration and distance traveled during that pretty small time interval. (a) In a time interval of $\Delta t=25\times 10^{-3}\,\rm s$, we are given the beginning velocity $v_1=0$ and the end velocity $v_2=85\,\rm m/s$. Because it is assumed the acceleration is constant, the average acceleration definition, $a=\frac{\Delta v}{\Delta t}$, is best suited for these known quantities. \begin{align*} a&=\frac{v_2-v_1}{\Delta t} \\\\ &=\frac{75-0}{25\times 10^{-3}} \\\\ &=3000\,\rm m/s^2 \end{align*} A huge acceleration is given to the tennis ball. (b) Here, we are asked to find the amount of distance traveled by the ball during the time the ball was in contact with the racket. Because we have a constant acceleration motion, it is best to use the following equation to find the distance traveled. \begin{align*} \Delta x&=\frac{v_1+v_2}{2}\times \Delta t \\\\ &=\frac{0+75}{2}\times (25\times 10^{-3}) \\\\ &=937.5\times 10^{-3}\,\rm m\end{align*} In millimeters, $\Delta x=937.5\,\rm mm$, and in centimeters $\Delta x=93.75\,\rm cm$. Therefore, during this incredibly short time interval, the ball moves about $94\,\rm cm$ along with the racket.

Starting from rest and ending at rest, a car travels a distance of $1500\,\rm m$ along the $x$-axis. During the first quarter of the distance, it accelerates at a rate of $+1.75\,\rm m/s^2$, while for the remaining distance, its acceleration is $-0.450\,\rm m/s^2$. (a) What is the time travel of the whole path? (b) What is the maximum speed of the car over this distance?

None of the time-dependent kinematics equations give us the time travel $t'$ without knowing the initial speed at the instant of the start of this second path.

We can find it using the equation $v^2-v_0^2=2a\Delta x$, setting $v=0$ at the end of the path, and solving for $v_0$ \begin{gather*} v^2-v_0^2=2a\Delta x \\\\ (0)^2-v_0^2=2(-0.450)(1125) \\\\ v_0=\sqrt{2\times 0.45\times 1125} \\\\ \Rightarrow v_0=31.82\,\rm m/s\end{gather*} Given that, one can use the simple equation $v=v_0+at$ and solve for the time travel in this part of the path. \begin{gather*} v=v_0+at \\\\ 0=31.82+(-0.450)t' \\\\ \Rightarrow t'=70.71\,\rm s\end{gather*} Therefore, the total time traveled over the entire path is the sum of these two times. \begin{align*} T&=t+t' \\\\ &=20.70+70.71 \\\\ &=\boxed{91.41\,\rm s} \end{align*}

A train that is $75$ meters long starts accelerating uniformly from rest. When the front of the train reaches a railway worker who is standing $150$ meters away from where the train started, it is traveling at a speed of $20\,\rm m/s$. What will be the speed of the last car as it passes the worker?

Solution : The front of the train is initially $150\,\rm m$ away from the worker, and when it passes him, it has a speed of $25\,\rm m/s$. From this data, we can find the acceleration of the front of the train (which is the same acceleration as the whole train) by applying the following kinematics equation \begin{gather*} v^2-v_0^2=2a\Delta x \\\\ (25)^2-(0)^2=2a\times 150 \\\\ \Rightarrow \quad a=2.08\,\rm m/s^2\end{gather*} Given the train's acceleration, now focus on the last car.

The last car is initially at rest and placed at a distance of $150+80=230\,\rm m$ away from the person. When it passes the person, it has traveled $\Delta x= 230\,\rm m$ and its speed is determined simply as below \begin{gather*} v^2-v_0^2=2a\Delta x \\\\ v^2-(0)^2=2(2.08)(230) \\\\ \Rightarrow \quad \boxed{v=30.93\,\rm m/s}\end{gather*}

A wildcat moving with constant acceleration covers a distance of $100\,\rm m$ apart in $8\,\rm s$. Assuming that its speed at the second point is $20\,\rm m/s$, (a) What was its speed in the first place? (b) At what rate does its speed change over this distance?

Solution : First of all, list all known data given to us. Time interval $\Delta t=8\,\rm s$, the horizontal displacement $\Delta x=100\,\rm m$, speed at second point $v_2=20\,\rm m/s$.

We are asked to find the speed at the second point. To solve this kinematics problem, we use the following kinematics equation because the acceleration is constant and this is the most relevant equation that relates the known to the unknown quantities. \begin{gather*} \Delta x=\frac{v_1+v_2}{2}\times \Delta t \\\\ 100=\frac{v_1+20}{2}\times 8 \\\\ \Rightarrow \quad \boxed{v_1=5\,\rm m/s} \end{gather*} Therefore, the wildcat's speed in the first place is $5\,\rm m/s$.

In this part, we should find the wildcat's acceleration because acceleration is defined as the time rate of change of the speed of a moving object. Given the first place speed, $v_1=5\,\rm m/s$, found in the preceding part, we can use the following time-independent kinematics equation to find the wanted unknown. \begin{gather*} v_2^2-v_1^2=2a\Delta x \\\\ (20)^2-(5)^2=2a(100) \\\\ \Rightarrow \quad \boxed{a=1.875\,\rm m/s^2}\end{gather*}

A car slows down uniformly from $45\,\rm m/s$ to rest in $10\,\rm s$. How far did it travel in this time interval?

Solution : List the data known as follows: initial speed $v_0=45\,\rm m/s$, final speed $v=0$, and the total time duration that this happened is $t=10\,\rm s$. The unknown is also the amount of displacement, $\Delta x$.

The only kinematics equation that relates those together is $\Delta x=\frac{v_1+v_2}{2}\times \Delta t$, where $v_1$ and $v_2$ are the velocities at the beginning and end of that time interval. \begin{align*} \Delta x&=\frac{v_1+v_2}{2}\times \Delta t \\\\ &=\frac{45+0}{2}\times 10 \\\\ &=\boxed{225\,\rm m}\end{align*} Keep in mind that we use this formula when the object slows down uniformly, or, in other words when the object's acceleration is constant.

Problem (5): We want to design an airport runway with the following specifications. The lowest acceleration of a plane should be $4\,{\rm m/s^2}$ and its take-off speed is 75 m/s. How long would the runway have to be to allow the planes to accelerate through it?

Solution: The known quantities are $a=4\,{\rm m/s^2}$, and final velocity $v=75\,{\rm m/s}$. The wanted quantity is runway length $\Delta x=x-x_0$. The perfect kinematics equation that relates those together is $v^2-v_0^2=2a(x-x_0)$. \begin{align*} v^2-v_0^2&=2a\Delta x\\\\ (75)^2-0&=2(4) \Delta x\\\\ \Rightarrow \Delta x&=\boxed{703\quad {\rm m}}\end{align*} Thus, if the runway wants to be effective, its length must be at least about 703 meters.

Problem (6): A stone is dropped vertically from a high cliff. After 3.55 seconds, it hits the ground. How high is the cliff?

Solution : There is another type of kinematics problem in one dimension but in the vertical direction. In such problems, the constant acceleration is that of free falling, $a=g=-10\,{\rm m/s^2}$.

"Dropped'' or "released'' in free-falling problems means the initial velocity is zero, $v_0=0$. In addition, it is always better to consider the point of release as the origin of the coordinate, so $y_0=0$.

The most relevant kinematics equation for these known and wanted quantities is $y=-\frac 12 gt^2+v_0t+y_0$ \begin{align*} y&=-\frac 12 gt^2+v_0t+y_0 \\\\&=-\frac 12 (9.8)(3.55)^2+0+0\\\\&=\boxed{-61.8\quad {\rm m}}\end{align*} The negative indicates that the impact point is below our chosen origin .

Problem (7): A ball is thrown into the air vertically from the ground level with an initial speed of 20 m/s. (a) How long is the ball in the air? (b) At what height does the ball reach?

Solution : The throwing point is considered to be the origin of our coordinate system, so $y_0=0$. Given the initial velocity $v_0=+20\,{\rm m/s}$ and the gravitational acceleration $a=g=-9.8\,{\rm m/s^2}$. The wanted time is how long it takes the ball to reach the ground again.

To solve this free-fall problem , it is necessary to know some notes about free-falling objects.

Note (1): Because the air resistance is neglected, the time the ball is going up is half the time it is going down.

Note (2): At the highest point of the path, the velocity of the object is zero.

(a) By applying the kinematics equation $v=v_0+at$ between the initial and the highest ($v=0$) points of the vertical path, we can find the going up time. \begin{align*} v&=v_0+at \\0&=20+(-9.8)t\\\Rightarrow t&=2.04\quad {\rm s}\end{align*} The total flight time is twice this time \[t_{tot}=2t=2(2.04)=4.1\,{\rm s}\] Hence, the ball takes about 4 seconds to reach the ground.

(b) The kinematics equation $v^2-v_0^2=2a(y-y_0)$ is best for this part. \begin{align*} v^2-v_0^2&=2a(y-y_0) \\0-20^2&=2(-9.8)(y-0) \\ \Rightarrow y&=\boxed{20\quad {\rm m}}\end{align*} Hence, the ball goes up to a height of about 20 meters.

Problem (8): An object moving in a straight line with constant acceleration, has a velocity of $v=+10\,{\rm m/s}$ when it is at position $x=+6\,{\rm m}$ and of $v=+15\,{\rm m/s}$ when it is at $x=10\,{\rm m}$. Find the acceleration of the object.

Solution : Draw a diagram, put all known data into it, and find a relevant kinematics equation that relates them together.

We want to analyze the motion in a distance interval of $\Delta x=x_2-x_1=10-6=4\,{\rm m}$, thus, we can consider the velocity at position $x_1=6\,{\rm m}$ as the initial velocity and at $x_2=10\,{\rm m}$ as the final velocity.

The most relevant kinematics equation that relates these known quantities to the wanted acceleration $a$ is $v^2-v_0^2=2a(x-x_0)$, where $x-x_0$ is the same given distance interval. Thus, \begin{align*} v^2-v_0^2&=2a(x-x_0) \\\\ (15)^2-(10)^2&=2(a)(4) \\\\225-100&=8a\\\\\Rightarrow a&=\frac{125}{8}\\\\&=15.6\,{\rm m/s^2}\end{align*}

Problem (9): A moving object accelerates uniformly from 75 m/s at time $t=0$ to 135 m/s at $t=10\,{\rm s}$. How far did it move at the time interval $t=2\,{\rm s}$ to $t=4\,{\rm s}$?

Solution : Draw a diagram and implement all known data in it as below.

Because the problem tells us that the object accelerates uniformly, its acceleration is constant along the entire path.

Given the initial and final velocities of the moving object, its acceleration is determined using the definition of instantaneous acceleration as below \[a=\frac{v_2-v_1}{t_2-t_1}=\frac{135-75}{10}=6\,{\rm m/s^2}\] In this kinematics problem, to analyze the motion between the requested times (stage II in the figure), we must have a little bit of information for that time interval, their velocities, or the distance between them.

As you can see in the figure, the initial velocity of stage II is the final velocity of stage I. By using a relevant kinematics equation that relates those data to each other, we would have \begin{align*} v&=v_0+at\\\\&=75+(6)(2) \\\\&=87\,{\rm m/s}\end{align*} This velocity would be the initial velocity for stage II of the motion. Now, all known information for stage II is initial velocity $v_0=87\,{\rm m/s}$, acceleration $a=6\,{\rm m/s^2}$, and time interval $\Delta t=2\,{\rm s}$. The wanted is the distance traveled $x=?$

The appropriate equation that relates all these together is $x=\frac 12 at^2+v_0t+x_0$. \begin{align*}x&=\frac 12 at^2+v_0t+x_0\\\\&=\frac 12 (6)(2)^2+(87)(2)+0\\\\&=186\quad {\rm m}\end{align*} Hence, our moving object travels a distance of 186 m between the instances of 2 s and 4 s.

Problem (10): From rest, a fast car accelerates with a uniform rate of $1.5\,{\rm m/s^2}$ in 4 seconds. After a while, the driver applies the brakes for 3 seconds, causing the car to uniformly slow down at a rate of $-2\,{\rm m/s^2}$. (a) How fast is the car at the end of the braking period? (b) How far has the car traveled after braking?

Solution : This motion is divided into two parts. First, draw a diagram and specify each section's known kinematics quantities.

(a) In the first part, given the acceleration, initial velocity, and time interval, we can find its final velocity at the end of 4 seconds. \begin{align*} v&=v_0+at\\&=0+(1.5)(4) \\&=6\quad {\rm m/s}\end{align*} This velocity is considered as the initial velocity for the second part, whose final velocity is wanted.

In the next part, the acceleration magnitude and braking time interval are given, so its final velocity is found as below \begin{align*} v&=v_0+at\\&=6+(-2)(3) \\&=0\end{align*} The zero velocity here indicates that the car, after the braking period, comes to a stop.

(b) The distance traveled in the second part is now calculated using the kinematics equation $x=\frac 12 at^2+v_0t+x_0$, because the only unknown quantity is distance $x$. \begin{align*} x&=\frac 12 at^2+v_0t+x_0\\\\&=\frac 12 (-2)(3)^2+(6)(3)+0\\\\&=+9\quad {\rm m}\end{align*} Therefore, after braking, the car traveled a distance of 9 meters before getting stopped.

Problem (11): A car moves at a speed of 20 m/s down a straight path. Suddenly, the driver sees an obstacle in front of him and applies the brakes. Before the car reaches a stop, it experiences an acceleration of $-10\,{\rm m/s^2}$. (a) After applying the brakes, how far did it travel before stopping? (b) How long does it take the car to reach a stop?

Solution : As always, the first and most important step in solving a kinematics problem is drawing a diagram and putting all known values into it, as shown below.

(a) The kinematics equation $v^2-v_0^2=2a(x-x_0)$ is the perfect equation as the only unknown quantity in it is the distance traveled $x$. Thus, \begin{align*} v^2-v_0^2&=2a(x-x_0) \\\\ 0^2-(20)^2&=2(-10)(x-0) \\\\\Rightarrow \quad x&=\frac {-400}{-20}\\\\&=20\quad {\rm m}\end{align*} (b) "how long does it take'' asks us to find the time interval. The initial and final velocities, as well as acceleration, are known, so the only relevant kinematics equation is $v=v_0+at$. Thus, \begin{align*} v&=v_0+at\\\\0&=20+(-10)t\\\\\Rightarrow t&=\frac{-20}{-10}\\\\&=2\quad {\rm s}\end{align*} Therefore, after braking, the car has moved for 2 seconds before reaching a stop.

Problem (12): A sports car moves a distance of 100 m in 5 seconds with a uniform speed. Then, the driver brakes, and the car, come to a stop after 4 seconds. Find the magnitude and direction of its acceleration (assumed constant).

Solution : uniform speed means constant speed or zero acceleration for the motion before braking. Thus, we can use the definition of average velocity to find its speed just before braking as below \begin{align*} \bar{v}&=\frac{\Delta x}{\Delta t}\\\\&=\frac{100}{5}\\\\&=20\quad {\rm m/s}\end{align*} Now, we know the initial and final velocities of the car in the braking stage. Since the acceleration is assumed to be constant, by applying the definition of average acceleration, we would have \begin{align*} \bar{a}&=\frac{v_2-v_1}{\Delta t}\\\\&=\frac{0-20}{4}\\\\&=-5\quad {\rm m/s^2}\end{align*} The negative shows the direction of the acceleration, which is toward the negative $x$-axis.

Hence, the car's acceleration has a magnitude of $5\,{\rm m/s^2}$ in the negative $x$ direction.

Problem (13): A race car accelerates from rest at a constant rate of $2\,{\rm m/s^2}$ in 15 seconds. It then travels at a constant speed for 20 seconds, and after that, it comes to a stop with an acceleration of $2\,{\rm m/s^2}$. (a) What is the total distance traveled by car? (b) What is its average velocity over the entire path?

Solution : To solve this kinematics question, we divided the entire path into three parts.

Part I: "From rest'' means the initial velocity is zero. Thus, given the acceleration and time interval, we can use the kinematics equation $v=v_0+at$ to calculate the distance traveled by car at the end of 15 seconds for the first part of the path. \begin{align*} x&=\frac{1}{2}at^2 +v_0 t+x_0\\\\&=\frac 12 (2)(15)^2 +(0)(15)+0\\\\&=\boxed{125\quad{\rm m}}\end{align*} As a side calculation, we find the final velocity for this part as below \begin{align*}v&=v_0+at\\\\&=0+(2) (15) \\\\&=30\quad {\rm m/s}\end{align*} Part II: the speed in this part is the final speed in the first part because the car continues moving at this constant speed after that moment.

The constant speed means we are facing zero acceleration. As a result, it is preferable to use the average velocity definition rather than the kinematics equations for constant (uniform) acceleration.

The distance traveled for this part, which takes 20 seconds at a constant speed of 30 m/s, is computed by the definition of average velocity as below \begin{align*} \bar{v}&=\frac{\Delta x}{\Delta t}\\\\30&=\frac{\Delta x}{20}\end{align*} Thus, we find the distance traveled as $\boxed{x=600\,{\rm m}}$.

Part III: In this part, the car comes to a stop, $v=0$, so its acceleration must be a negative value as $a=-2\,{\rm m/s^2}$. Here, the final velocity is also zero. Its initial velocity is the same as in the previous part.

Consequently, the best kinematics equation that relates those known to the wanted distance traveled $x$, is $v^2-v_0^2=2a(x-x_0)$. \begin{align*} v^2-v_0^2&=2a(x-x_0) \\\\0^2-(30)^2&=2(-2)(x-0) \\\\ \Rightarrow \quad x&=\boxed{225\quad {\rm m}}\end{align*} The total distance traveled by car for the entire path is the sum of the above distances \[D=125+600+225=\boxed{950\quad {\rm m}}\]

Problem (14): A ball is dropped vertically downward from a tall building of 30-m-height with an initial speed of 8 m/s. After what time interval does the ball strike the ground? (take $g=-10\,{\rm m/s^2}$.)

Solution : This is a free-falling kinematics problem. As always, choose a coordinate system along with the motion and the origin as the starting point.

Here, the dropping point is considered the origin, so in all kinematics equations, we set $y_0=0$. By this choice, the striking point is 30 meters below the origin, so in equations, we also set $y=-30\,{\rm m}$.

Remember that velocity is a vector in physics whose magnitude is called speed. In this problem, the initial speed is 8 m/s downward. This means that the velocity vector is written as $v=-8\,{\rm m/s}$.

Now that all necessary quantities are ready, we can use the kinematics equation $y=\frac 12 at^2+v_0t+y_0$, to find the wanted time that the ball strikes the ground. \begin{align*} y&=\frac 12 at^2+v_0t+y_0\\\\-30&=\frac 12 (-10)t^2+(-8)t+0\end{align*} After rearranging, a quadratic equation like $5t^2+8t-30=0$ is obtained, whose solutions are given as below: \begin{gather*} t=\frac{-8\pm\sqrt{8^2-4(5)(-30)}}{2(5)}\\\\ \boxed{t_1=1.77\,{\rm s}} \quad , \quad t_2=-3.37\,{\rm s}\end{gather*} $t_1$ is the accepted time because the other is negative, which is not acceptable in kinematics. Therefore, the ball takes about 1.7 seconds to hit the ground.

Note: The solutions of a quadratic equation like $at^2+bt+c=0$, where $a,b,c$ are some constants, are found by the following formula: \[t=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\]

Problem (15): The acceleration versus time graph for an object that moves at a constant speed of 30 m/s is shown in the figure below. Find the object's average velocity between instances $t_1=10\,{\rm s}$ and $t_2=30\,{\rm s}$.

Solution : The best and shortest approach to solving such a kinematics problem is to first draw its velocity-vs-time graph. Next, the area under the obtained graph gives us the total displacement, which is divided by the total time interval to yield the average velocity.

The path consists of three parts with different accelerations.

In the first part, the object slows down its motion at a constant rate of $-2\,{\rm m/s^2}$ in 10 seconds. Its initial velocity is also 30 m/s. With these known quantities in hand, the kinematics equation $v=v_0+at$ gives us the velocity at the end of this time interval. \begin{align*} v&=v_0+at\\&=30+(-2)(10) \\&=10\quad {\rm m/s}\end{align*} This calculation corresponds to a straight line between the points $(v=30\,{\rm m/s},t=0)$ and $(v=10\,{\rm m/s},t=10\,{\rm s})$ on the $v-t$ graph as shown below.

Next, the object moves with zero acceleration for 5 seconds, which means the velocity does not change during this time interval. This implies that we must draw a horizontal line in the $v-t$ graph.

In the last part, the object accelerates from 10 m/s with a constant rate of $+2\,{\rm m/s^2}$ in 15 seconds. Thus, its final velocity at the end of this time interval is determined as below \begin{align*} v&=v_0+at\\&=10+(2)(15) \\&=40\quad {\rm m/s}\end{align*} Now, it's time to draw the velocity-vs-time graph. As an important point, note that all these motions have a constant acceleration, so all parts of a velocity-time graph, are composed of straight-line segments with different slopes.

For part I, we must draw a straight-line segment between the velocities of 30 m/s and 10 m/s.

Part II is a horizontal line since its velocities are constant during that time interval, and finally, in Part III, there is a straight line between velocities of 10 m/s and 40 m/s.

All these verbal phrases are illustrated in the following velocity-vs-time graph .

Recall that the area under a velocity vs. time graph always gives the displacement. Hence, the area under the $v-t$ graph between 10 s and 30 s gives the displacement. Therefore, the areas of rectangle $S_1$ and trapezoid $S_2$ are calculated as below \begin{gather*} S_1 =10\times 5=50\quad {\rm m} \\\\S_2=\frac{10+40}{2}\times 15=375\quad {\rm m}\end{gather*} Therefore, the total displacement in the time interval $[15,30]$ is \[D=S_{tot}=S_1+S_2=425\,{\rm m}\] From the definition of average velocity, we have \[\bar{v}=\frac{displacement}{time}=\frac{425}{20}=21.25\,{\rm m/s}\]

In this tutorial, all concepts about kinematics equations are taught in a problem-solution strategy. All these answered problems are helpful for MCAT physics exams.

We can also find these kinematic variables using a position-time or velocity-time graph. Because slopes in those graphs represent velocity and acceleration, respectively, and the concavity of a curve in a position vs. time graph shows the sign of its acceleration in an x-t graph as well.

Author : Dr. Ali Nemati Date published : 8-7-2021 Updated : June 12, 2023

© 2015 All rights reserved. by Physexams.com

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## Mechanics: 1-Dimensional Kinematics

Calculator pad, version 2, 1-d kinematics problem set.

In the 2008 Olympics, Jamaican sprinter Usain Bolt shocked the world as he ran the 100-meter dash in 9.69 seconds. Determine Usain's average speed for the race.

- Audio Guided Solution
- Show Answer

In the Funny Car competition at the Joliet Speedway in Joliet, Illinois in October of 2004, John Force complete the Â¼-mile dragster race in a record time of 4.437 seconds. Determine the average speed of the dragster in mi/hr and m/s. GIVEN: (1.000 mi =1609 m)

In the qualifying round of the 50-yd freestyle in the sectional swimming championship, Dugan got an early lead by finishing the first 25.00 yd in 10.01 seconds. Dugan finished the return leg (25.00 yd distance) in 10.22 seconds.

a. Determine Dugan's average speed for the entire race. b. Determine Dugan's average speed for the first 25.00 yd leg of the race. c. Determine Dugan's average velocity for the entire race.

In last week's Homecoming victory, Al Konfurance, the star halfback of South's football team, broke a tackle at the line of scrimmage and darted upfield untouched. He averaged 9.8 m/s for an 80-yard (73 m) score. Determine the time for Al to run from the line of scrimmage to the end zone.

During the annual shuffleboard competition, Renee gives her puck an initial speed of 9.32 m/s. Once leaving her stick, the puck slows down at a rate of -4.06 m/s/s.

a. Determine the time it takes the puck to slow to a stop. b. Use your initial speed and the calculated time to determine the average speed and the distance which the puck travels before stopping.

Ken Runfast is the star of the cross-country team. During a recent morning run, Ken averaged a speed of 5.8 m/s for 12.9 minutes. Ken then averaged a speed of 6.10 m/s for 7.1 minutes. Determine the total distance which Ken ran during his 20 minute jog.

The Lamborghini Murcielago can accelerate from 0 to 27.8 m/s (100 km/hr or 62.2 mi/hr) in a time of 3.40 seconds. Determine the acceleration of this car in both m/s/s and mi/hr/s.

Homer Agin leads the Varsity team in home runs. In a recent game, Homer hit a 96 mi/hr sinking curve ball head on, sending it off his bat in the exact opposite direction at 56 mi/hr. The actually contact between ball and bat lasted for 0.75 milliseconds. Determine the magnitude of the average acceleration of the ball during the contact with the bat. Express your answer in both mi/hr/s and in m/s/s. (Given: 1.00 m/s = 2.24 mi/hr)

A Formula One car is a single-seat racing car with an open cockpit and substantial wings located in the front and rear. At high speeds, the aerodynamics of the car help to create a strong downward force which allows the car to brake from 27.8 m/s (100 km/hr or 62.2 mi/hr) to 0 in as small of a distance as 17 meters. Determine the deceleration rate (i.e., acceleration) achieved by such a car.

The position-time graph below represents the motion of South's basketball coach during the last sixteen seconds of overtime during this past weekend's game.

Use the graph to answer the next several questions.

a. Determine the total distance walked by the coach during these 16 seconds. b. Determine the resulting displacement of the coach during these 16 seconds. c. Determine the displacement of the coach after 12.0 seconds. d. At what time did the coach have the greatest displacement from his starting position? e. What was the fastest speed which the coach walked during any of the time intervals for the last 16.0 seconds? f. What was the average speed of the coach for these 16.0 seconds?

Mr. H is preparing to show the class a Strobe demonstration when he realizes that his absent-mindedness has struck once more. He left the strobe on the counter in the back of the lab after the last class period. Starting 1.0 meter from the front of the room, Mr. H walks quickly to the back of the lab, picks up the strobe and returns to the middle of the classroom. The position-time graph below represents his motion. Use the graph to answer the next several questions.

a. What is the total distance walked by Mr. H during these 8.0 seconds? b. What is the average speed of Mr. H during these 8.0 seconds? c. What is the average velocity of Mr. H during these 8.0 seconds? d. How fast did Mr. H walk during the first 5.0 seconds? e. How fast did Mr. H walk during the last 3.0 seconds?

The position-time graph below represents the motion of two students - Mac (in red) and Tosh (in blue) - as they enter and exit the school library during a passing period.

Use the graph to determine the speeds at which the two students move. (Ignore any stationary periods of time.) Then determine how much faster the fastest student moves than the slower student.

Renatta Gas did it again. She failed to fill up her tank during the last four weeks. The velocity-time graph below represents the last six seconds of motion her car before being stranded on a highway in route to her university.

Use this graph to determine...

a. ...the acceleration of Renatta's car. b. ...the distance traveled during her last 6.0 seconds of motion.

Marcus Tardee is driving his friends to school. With the start of school being only minutes away, he is unfortunately following a slow garbage truck. The truck finally turns down a side street and Marcus accelerates to a much more customary speed. The velocity-time graph below represents his motion. Use the graph to answer the following questions.

a. How fast was Marcus traveling while following the garbage truck? b. Determine the distance traveled during the first 4.0 seconds represented on the graph. c. Determine the acceleration of the car once the garbage truck turned onto the side street. d. Determine the distance traveled by the car during the last 6.0 seconds of motion.

The velocity-time graph below represents the motion of a car on a city street.

Use the graph to determine the acceleration values of the car at ...

a. 1.4 seconds. b. 6.8 seconds. c. 11.6 seconds. d. 17.6 seconds.

After a long soccer practice down at the neighborhood soccer fields, Suzie begins walking up the steep hill towards her home. She gives her soccer ball a kick up the hill and continues walking towards it, meeting the ball as it is rolling back down. The velocity-time graph below depicts the motion of the ball. Use the graph to answer the following questions.

a. At what time did the ball change directions and begin rolling back down the hill? b. What is the acceleration of the ball as it rolls up the hill? down the hill? c. How far up the hill did the ball roll before it began to roll back down? d. Determine the total distance traveled by the ball during the 5.00 seconds - both the distance up the hill and down the hill. e. How far up the hill did Suzie walk between the time when she kicked the ball and the time she met up with the ball (at 5.0 seconds)?

Jeremy has recently taken up snowboarding as a hobby. He is practicing making smooth turns while traveling up sloped inclines. The velocity-time graph below depicts his motion traveling up an embankment and part-way down. Use the graph to answer the following questions.

a. Determine Jeremy's acceleration at 8.0 seconds. b. Determine the distance Jeremy traveled from 0.0 to 5.0 seconds. c. At what time did Jeremy begin to travel back down the embankment?

A Cessna 150 airplane has a takeoff speed of 28 m/s (63 mi/hr). Determine the minimum length of the runway which would be required for the plane to take off if it averages an acceleration of 1.9 m/s/s.

Cynthia competes in luge competitions during the winter months. She rides solo on a small sled 3 inches off the ground down icy slopes, turning only by use of her feet and the shifting of her weight on the sled. During the initial stage of one downhill luge, Cynthia accelerated from rest at 6.84 m/s/s for 2.39 seconds. Determine the distance she moved during this acceleration phase.

Suzie Lavtaski has reached the end of the ski slope and abruptly decelerates from 29.0 m/s to 1.8 m/s in 1.45 seconds. Determine Suzie' acceleration rate and the distance she moved during this braking period.

Captain John Stapp is often referred to as the "fastest man on Earth." In the late 1940s and early 1950s, Stapp ran the U.S. Air Force's Aero Med lab, pioneering research into the accelerations which humans could tolerate and the types of physiological effects which would result. After several runs with a 185-pound dummy named Oscar Eightball, Captain Stapp decided that tests should be conducted upon humans. Demonstrating his valor and commitment to the cause, Stapp volunteered to be the main subject of subsequent testing.

Manning the rocket sled on the famed Gee Whiz track, Stapp tested acceleration and deceleration rates in both the forward-sitting and backward-sitting positions. He would accelerate to aircraft speeds along the 1200-foot track and abruptly decelerate under the influence of a hydraulic braking system. On one of his most intense runs, his sled decelerated from 282 m/s (632 mi/hr) to a stop at -201 m/s/s. Determine the stopping distance and the stopping time.

Julietta and Jackson are playing miniature golf. Julietta's ball rolls into a long. straight upward incline with a speed of 2.95 m/s and accelerates at -0.876 m/s/s for 1.54 seconds until it reaches the top of the incline and then continues along an elevated section. Determine the length of the incline.

Rickey Henderson, baseball's record holder for stolen bases, approaches third base. He dives head first, hitting the ground at 6.75 m/s and reaching the base at 5.91 m/s, accelerating at -5.11 m/s/s. Determine the distance Rickey slides across the ground before touching the base.

Win Blonehare and Kent Swimtashore are sailboating in Lake Gustastorm. Starting from rest near the shore, they accelerate with a uniform acceleration of 0.29 m/s/s, How far are they from the shore after 18 seconds?

For years, the tallest tower in the United States was the Phoenix Shot Tower in Baltimore, Maryland. The shot tower was used from 1828 to1892 to make lead shot for pistols and rifles and molded shot for cannons and other instruments of warfare. Molten lead was dropped from the top of the 234-foot (71.3 meter) tall tower into a vat of water. During its free fall, the lead would form a perfectly spherical droplet and solidify. Determine the time of fall and the speed of a lead shot upon hitting the water at the bottom.

According to Guinness, the tallest man to have ever lived was Robert Pershing Wadlow of Alton, Illinois. He was last measured in 1940 to be 2.72 meters tall (8 feet, 11 inches). Determine the speed which a quarter would have reached before contact with the ground if dropped from rest from the top of his head.

A California Condor is approaching its nest with a large chunk of carrion in its beak. As it approaches, it makes an upward swoop, achieving a momentary upward velocity of 12.8 m/s when the carrion falls from its mouth, hitting a cliff outcropping 32.1 m below. Determine the speed of the carrion upon hitting the outcropping.

During his recent skydiving adventure, Luke Autbeloe had reached a terminal speed of 10.4 m/s as he approached the ground with his parachute. During an attempt to snap one last photo with his camera, Luke fumbled it from a height of 52.1 m above the ground.

a. Determine the speed with which the camera hits the ground. b. Determine the time for the camera to free fall from Luke's hands to the ground.

The speed required of a military jet when taking off from the deck of an aircraft carrier is dependent upon the speed of the carrier and the speed of the wind into which the carrier is moving. The takeoff speed required of a military jet relative to the deck of the carrier is 45 m/s when the carrier travels at 45 mi/hr into a 20 mi/hr wind. And when the aircraft carrier is traveling at 10 mi/hr into a 5 mi/hr wind, the takeoff speed relative to the deck of the carrier is 71 m/s. Determine the acceleration which a military jet must have to take off under these two conditions from the 126-m long runway of the USS Ronald Reagan aircraft carrier.

The Zero Gravity Research Facility at NASA-operated Glenn Research Center in Ohio is used to test the behavior of fluids, flames, equipment and other objects in free fall. It consists of a 467-foot long, 12-foot diameter, steel vacuum chamber. The steel chamber resides inside of a concrete lined shaft which extends 510 feet below ground level. Objects falling through the tower experience free fall over a distance of 432 feet (132 meters).

a. Determine the falling time for objects dropped from rest. b. Determine the final speed of the objects before the braking period begins.

It's breakfast time and Mr. H entertains himself once more by watching the daily beetle race across the 35.7-cm length of the Wheaties box top. Angie the beetle typically averages 3.77 mm/s and Bessie the beetle averages 4.78 mm/s. If Bessie gives Angie a 5.4 cm head start, then which beetle wins and by what distance?

Alexander's hobby is dirt biking. On one occasion last weekend, he accelerated from rest to 17.8 m/s/s in 1.56 seconds. He then maintained this speed for 9.47 seconds. Seeing a coyote cross the trail ahead of him, he abruptly stops in 2.79 seconds. Determine Alexander's average speed for this motion.

Ima Rushin can travel from Milwaukee Avenue to the school entrance gate at a constant speed of 22.5 m/s when the lights are green and there is no traffic. On Wednesday, Ima is stopped by a red light at Landwehr Road. She decelerates at -3.95 m/s/s, waits for 45.0 seconds before the light turns green and accelerates back up to speed at 4.91 m/s/s.

a. Determine the total time required to decelerate, stop and accelerate back up to speed. b. Determine the amount of time the red light costs the driver (compared to if the car had not been stopped by the red light).

A tortoise and a hare are having a 1000-meter race. The tortoise runs the race at a constant speed of 2.30 cm/s. The hare moves at an average speed of 1.50 m/s for 10.0 minutes and then decides to take a nap. After waking up from the nap, the hare recognizes that the tortoise is about to cross the finish line and immediately accelerates from rest with a constant acceleration of 0.500 m/s/s for the remaining distance of the race. If the tortoise wins by a hair (no pun intended), then what is the time in hours that the hare napped?

Hayden and Matthew are riding around the neighborhood on their scooters. Hayden is at rest when Matthew passes him moving at a constant speed of 0.37 m/s. After 1.8 seconds, Hayden decides to chase after Matthew, accelerating at 0.91 m/s/s. How much time must Hayden accelerate before he is side-by-side with Matthew?

## View Audio Guided Solution for Problem:

## Browse Course Material

Course info, instructors.

- Prof. Deepto Chakrabarty
- Dr. Peter Dourmashkin
- Dr. Michelle Tomasik
- Prof. Anna Frebel
- Prof. Vladan Vuletic

## Departments

As taught in.

- Classical Mechanics

## Learning Resource Types

Week 1: kinematics.

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- Week 1: Introduction

## Lesson 1: 1D Kinematics - Position and Velocity

- 1.1 Coordinate Systems and Unit Vectors in 1D Position Vector in 1D
- 1.2 Position Vector in 1D
- 1.3 Displacement Vector in 1D
- 1.4 Average Velocity in 1D
- 1.5 Instantaneous Velocity in 1D
- 1.6 Derivatives
- 1.7 Worked Example - Derivatives in Kinematics

## Lesson 2: 1D Kinematics - Acceleration

- 2.1 Introduction to Acceleration
- 2.2 Acceleration in 1D
- 2.3 Worked Example - Acceleration from Position
- 2.4 Integration
- 2.5 List of Useful Integrals

## Lesson 3: 2D Kinematics - Position, Velocity, and Acceleration

- 3.1 Coordinate System and Position Vector in 2D
- 3.2 Instantaneous Velocity in 2D
- 3.3 Instantaneous Acceleration in 2D
- 3.4 Projectile Motion
- 3.5 Demos for Projectile Motion

## Week 1 Worked Examples

- PS.1.1 Three Questions Before Starting
- PS.1.2 Shooting the Apple
- PS.1.3 Worked Example: Braking Car
- PS.1.4 Sketch the Motion
- PS.1.5 Worked Example: Pedestrian and Bike at Intersection

## Week 1 Problem Set

- Problem Set 1

Mr. Lam's Classroom

## Physics 11 – Kinematics

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## AP®︎/College Physics 1

Welcome to ap/college physics 1, unit 1: kinematics and introduction to dynamics, unit 2: newton's laws, unit 3: circular motion and gravitation, unit 4: energy and momentum, unit 5: simple harmonic motion and rotational motion.

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## Kinematics Practice Problems

Showing top 8 worksheets in the category - Kinematics Practice Problems .

Some of the worksheets displayed are Kinematics practice problems, Student work for two dimensional kinematics, Physics kinematics objectives students will be able to, Test1 ch15 kinetics practice problems, Kinetics practice problems and solutions, Topic kinematics, Chapter 3 kinematics in two or three dimensions vectors, Kinematics practice problems work answer key.

Once you find your worksheet, click on pop-out icon or print icon to worksheet to print or download. Worksheet will open in a new window. You can & download or print using the browser document reader options.

## 1. Kinematics practice problems

2. student worksheet for two dimensional kinematics, 3. physics kinematics objectives students will be able to, 4. test1 ch15 kinetics practice problems, 5. kinetics practice problems and solutions, 6. topic 3.1: kinematics, 7. chapter 3 kinematics in two or three dimensions; vectors, 8. kinematics practice problems worksheet answer key.

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## Kinematics Practice Problems

Displaying top 8 worksheets found for - Kinematics Practice Problems .

Some of the worksheets for this concept are Kinematics practice problems, Student work for two dimensional kinematics, Physics kinematics objectives students will be able to, Test1 ch15 kinetics practice problems, Kinetics practice problems and solutions, Topic kinematics, Chapter 3 kinematics in two or three dimensions vectors, Kinematics practice problems work answer key.

Found worksheet you are looking for? To download/print, click on pop-out icon or print icon to worksheet to print or download. Worksheet will open in a new window. You can & download or print using the browser document reader options.

## 1. Kinematics practice problems

2. student worksheet for two dimensional kinematics, 3. physics kinematics objectives students will be able to, 4. test1 ch15 kinetics practice problems, 5. kinetics practice problems and solutions, 6. topic 3.1: kinematics, 7. chapter 3 kinematics in two or three dimensions; vectors, 8. kinematics practice problems worksheet answer key.

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## IMAGES

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## COMMENTS

These problems allow any student of physics to test their understanding of the use of the four kinematic equations to solve problems involving the one-dimensional motion of objects. You are encouraged to read each problem and practice the use of the strategy in the solution of the problem.

Solution: First of all, collect the given data in the interval of accelerating initial velocity = 30 m/s final velocity = 0 overall time = 7.20 s distance =? One can solve this problem in two, direct and indirect, ways. In one way, first, find the acceleration of the car and then use other kinematic equations to deter- mine the desired quantity.

Kinematics Practice Problems: Problem (1): A car slows down its motion from 10 m/s to 6 m/s in 2 seconds under constant acceleration. (a) What is its acceleration? (b) How far did the car travel during this time interval? Solution: This is the simplest kinematics problem, so we put a bit more time to solve it in detail.

Problem 1 In the 2008 Olympics, Jamaican sprinter Usain Bolt shocked the world as he ran the 100-meter dash in 9.69 seconds. Determine Usain's average speed for the race. Audio Guided Solution Show Answer Problem 2

Problem 1. A runner accelerates to 4.2 m/s2 for 10 seconds before winning the race. How far did he/she run? Problem 2. A plane starts from rest and accelerates uniformly over a time of 20 s for a distance of 300 m. Determine the plane's acceleration. Problem 3. A ball free falls from the top of the roof for 5 seconds. How far did it fall?

Kinematics Practice Problems Name:_______________ Block:____ Date:__________ Kinematics is the study of motion. In 1-D motion, most every kinematic problem can be solved using one of 4 equations. These equations will allow you to solve for almost any aspect of the motion of an object: displacement, velocity and acceleration.

Determine the distance covered by the motorcycle in the first 8 seconds. 4 PRACTICE PROBLEM A box sliding at a constant speed of 5.0 m/s on a frictionless surface enters a rough, concrete surface. When the box moves 3.0 meters on concrete, its speed drops to 4.0 m/s. Determine the magnitude of deceleration of the box on concrete. 5 PRACTICE PROBLEM

a. Give a written description of the motion. b. Determine the displacement from t = 0s to t = 4 s. c. Determine the displacement from t = 2 s to t = 6 s. d. Determine the object's acceleration at t =4s. e. Sketch a possible x-t graph for the motion of the object. Label the axis. Explain why your graph is only one of many possible graphs. 2.

Science Kinematic formulas in one-dimension Google Classroom You might need: Calculator A child blows a leaf straight up in the air. The leaf reaches 1.0 m higher than its original height with a constant acceleration of 1.0 m s 2 upward. How much time did it take the leaf to get displaced by 1.0 m ?

Uniformly Accelerated Motion. Directions: On this worksheet you will practice solving problems by using the five basic kinematics equations for uniformly accelerated motion. omit. Question 1 Scenario #1: A car accelerates uniformly from rest to a final speed of 21 m/sec in 11 seconds. How far does it travel during this period of acceleration ...

Choose 1 answer: 2.4 m s A 2.4 m s 8.6 m s B 8.6 m s 5.4 m s C 5.4 m s 7.0 m s D 7.0 m s Show Calculator Stuck? Use a hint. Do 4 problems Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more.

1. In kinematics, how do we resolve questions of motion? Through charts and pictorial representations Through geometric equations Through repeatable experiments Through lucky guesses 2. Which of...

Question 1. A bus start at Station A from rest with uniform acceleration 2m/sec 2 .Bus moves along a straight line a. Find the distance moved by the bus in 10 sec? b. At what time, it velocity becomes 20m/sec? c. How much time it will take to cover a distance of 1.6km Solution Question 2. A object is moving along an straight line.

Lesson 1: 1D Kinematics - Position and Velocity. 1.1 Coordinate Systems and Unit Vectors in 1D Position Vector in 1D. 1.2 Position Vector in 1D. 1.3 Displacement Vector in 1D. 1.4 Average Velocity in 1D. 1.5 Instantaneous Velocity in 1D. 1.6 Derivatives. 1.7 Worked Example - Derivatives in Kinematics.

Rotational kinematics. A merry-go-round has an initial angular velocity of 10.2 rpm . At the end of the ride, the brakes are applied, giving it a constant angular deceleration of 0.032 rad/s 2 as the ride slows to a stop. Determine the angular velocity of the ride, in rad/s , after it has made two revolutions during the braking period.

practice problem 1 I went for a walk one day. I walked north 6.0 km at 6.0 km/h and then west 10 km at 5.0 km/hr. (This problem is deceptively easy, so be careful. Begin each part by reviewing the appropriate physical definition.) Determine… the total distance of the entire trip the total displacement of the entire trip

Learn Kinematics in 2D with free step-by-step video explanations and practice problems by experienced tutors.

Learn Kinematics Equations with free step-by-step video explanations and practice problems by experienced tutors. ... Table of contents. 0. Math Review 31m. Worksheet. Math Review 31m. 1. Intro to Physics Units 51m. Worksheet. Introduction to Units 17m. Unit Conversions 7m. Solving Density Problems 7m. Dimensional Analysis 5m. Counting ...

6. 16 Feb 2023. (Thu) Notes: Graphs of Motion (Velocity vs. Time) Worksheet: Graphs of Motion II ( solutions) Assignment: Kinematics Video Analysis due next class (print and bring to class) Lab: Acceleration due to Gravity Lab complete Introduction pre-lab questions for next class. In-Class Questions. Zitzewitz: §5.2.

AP®︎/College Physics 1 5 units · 27 skills. Unit 1 Kinematics and introduction to dynamics. Unit 2 Newton's laws. Unit 3 Circular motion and gravitation. Unit 4 Energy and momentum. Unit 5 Simple harmonic motion and rotational motion. Course challenge. Test your knowledge of the skills in this course. Start Course challenge.

Showing top 8 worksheets in the category - Kinematics Practice Problems. Some of the worksheets displayed are Kinematics practice problems, Student work for two dimensional kinematics, Physics kinematics objectives students will be able to, Test1 ch15 kinetics practice problems, Kinetics practice problems and solutions, Topic kinematics, Chapter 3 kinematics in two or three dimensions vectors ...

Displaying top 8 worksheets found for - Kinematics Practice Problems. Some of the worksheets for this concept are Kinematics practice problems, Student work for two dimensional kinematics, Physics kinematics objectives students will be able to, Test1 ch15 kinetics practice problems, Kinetics practice problems and solutions, Topic kinematics, Chapter 3 kinematics in two or three dimensions ...

21 PRACTICE PROBLEM. Determine the electric field strength at two distinct points within a solenoid: (i) At a point directly on the axis (ii) At a point located 1.0 cm away from the axis. The solenoid has a diameter of 6.0 cm and the magnetic field inside the solenoid is 3.0 T, diminishing at a rate of 2.0 T/s.

50 Kinematics Practice Problems Worksheet October 19, 2019 May 4, 2019 by chess93 Kinematics Worksheet With Answers from kinematics practice problems worksheet , image source: briefencounters.ca