The example problems are all uniquely numbered for easy reference. The problem statement is given, and then the solution is provided as a PDF file which you can download.

If you want to review the theory behind all these problems, I conveniently cover that on this website, in the kinematics and dynamics pages. Note that this page is a work in progress and new content will be added regularly.

To see the example problems click on the category you are interested in:

Kinematics – 1-D problems involving free-fall acceleration (motion along a straight line) – Senior high school and first year college/university

Kinematics – 1-D problems involving constant acceleration (motion along a straight line) – Senior high school and first year college/university

Kinematics – 1-D problems involving average velocity and average speed (motion along a straight line) – Senior high school and first year college/university

Kinematics – 1-D problems involving instantaneous velocity and speed (motion along a straight line) – Senior high school and first year college/university

Kinematics – 1-D problems involving average acceleration and instantaneous acceleration (motion along a straight line) – Senior high school and first year college/university

Problem # 1:

A building is under construction, and a construction worker is standing on top of a 130 m high elevator shaft. The worker accidentally drops his hammer down the shaft.

(a) At what speed does the hammer hit the ground?

(b) How much time passes between when the hammer is dropped and when it hits the ground?

(c) What fraction of the total airborne time does the hammer spend in the top 75% of the falling distance?

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Problem # 2:

A model rocket is launched vertically, and has a constant acceleration of 5.0 m/s

(a) What is the maximum height reached by the rocket?

(b) How much time passes between when the rocket is launched and when it lands?

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Problem # 3:

An object is dropped from rest, and one second before it lands it is at half its initial drop height.

(a) What is the falling time?

(b) What is the drop height?

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Problem # 4:

A ball is thrown vertically upward. On its way up it passes point A at a speed

(a) What is the speed

(b) What is the distance between point A and the peak height reached by the ball?

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Problem # 5:

A drop tower at an amusement park rises at 5 m/s and is 45 m above the ground when one of the riders drops her phone.

(a) How long does it take for the phone to fall to the ground?

(b) At what speed does the phone hit the ground?

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Problem # 6:

A girl is standing in an elevator moving upward at 5 m/s. She places a launch toy on the floor of the elevator, which then launches a ball straight up at 5.5 m/s relative to the elevator. The girl catches the ball 1.0 seconds later. At the instant the ball is caught, the floor of the elevator is 32 m above the ground.

(a) What is the height of the ball above the ground at the instant it is caught?

(b) What is the height of the elevator floor above the ground at the instant the ball is launched?

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Problem # 7:

A child is standing in an elevator with glass walls, at a mall. She throws a ball in the air at a vertical upward speed of 4.5 m/s relative to the elevator, and from a height of 1.3 m relative to the elevator floor. At the same time, the elevator is moving upward at 3 m/s, starting from ground level.

(a) From the perspective of the child, what is the maximum height reached by the ball?

(b) From the perspective of someone in the mall (outside the elevator), what is the maximum height reached by the ball?

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Problem # 8:

A mischievous student drops an egg from the window of his dorm room. The egg falls straight down onto the hood of a car parked below. A few floors below, someone is recording a video on their webcam, which is facing the window. The egg is recorded falling past the window. The person recording the video is a physics student, and she sees an opportunity to solve an interesting physics problem while also determining the height, and consequently the room, that the egg was dropped from. She analyzes the video, and determines that it took the egg 0.14 seconds to fall from the top of the window to the bottom. She then measures the height of the window to be 1.30 meters. From what height, measured from the top of the window, was the egg dropped?

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Problem # 9:

A game is played by two children, in which one child, at a height of 10 m above the ground, drops a rock with no initial speed. The second child also drops a rock, from a height of 15 m above the ground. The second child drops the rock

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Problem # A-1:

A car travelling on a straight road at 25 m/s undergoes constant acceleration until it reaches a speed of 40 m/s. The car then maintains this speed for 6.0 seconds. The brakes are then applied, causing the car to undergo constant deceleration until it once more reaches a speed of 25 m/s. If it takes the car 25 seconds from the time that it starts accelerating to the time that it slows down to 25 m/s, how far does it travel in this time?

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Problem # A-2:

A train is moving at high speed on a straight track, while at the same time a locomotive is moving in the opposite direction on the same track. In order to avoid a collision, the locomotive must move on to the siding before a collision becomes unavoidable. At the same time, the train must decelerate by putting the brakes on. At the instant shown, the front of the train is 0.35 mi from the back of the locomotive, the back of the locomotive is 0.1 mi from the siding entrance, the speed of the train is 80 mi/h, and the maximum speed of the locomotive is 20 mi/h. What is the minimum deceleration of the train?

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Problem # A-3:

Given the above graph of

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Problem # A-4:

The takeoff speed of a commercial jet is 260 km/h. If the runway is 2.1 km long, what is the minimum constant acceleration of the jet?

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Problem # A-5:

A truck driving on a paved road is capable of decelerating at a constant value of 5 m/s

(a) If the truck is initially travelling at 27.4 m/s, how long does it take to come to a complete stop?

(b) How far does the truck travel in this time?

(c) Sketch a graph of distance vs. time and speed vs. time, when the brakes are applied.

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Problem # A-6:

A distracted driver is cruising at 25 m/s when she suddenly notices a truck directly ahead moving at 15 m/s, in the same direction. At the instant she brakes, the distance between the front of the car and the back of the truck is

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Problem # A-7:

A distracted driver is cruising at 25 m/s when he suddenly notices a truck directly ahead moving at 15 m/s, in the same direction. At the instant he brakes, the distance between the front of the car and the back of the truck is 15 m. If the car decelerates at

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Problem # A-8:

A distracted driver is cruising at 25 m/s when he suddenly notices a truck directly ahead moving at 15 m/s, in the same direction. At the instant he brakes, the distance between the front of the car and the back of the truck is 9 m. The car decelerates at 5 m/s

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Problem # A-9:

A distracted driver is driving on the wrong side of the road, when he notices an oncoming vehicle moving towards him. He quickly applies the brakes, causing his car to decelerate at 4.5 m/s

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Problem # B-1:

The speed of sound in air is 330 m/s at 0 degrees Celsius. If the average velocity of a jet plane is 2.3 times the speed of sound, how far does it travel in 0.25 seconds?

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Problem # B-2:

A delivery truck travels up a hill at a constant speed of 50 km/h, in order to deliver a package. After the package is delivered, the truck travels down the same hill at 80 km/h. What is the average speed of the truck for the round trip?

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Problem # B-3:

The graph shown above shows velocity vs. time for a particle moving along a straight line. What is the average velocity and average speed for the particle for the entire time the particle is in motion?

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Problem # B-4:

A particle is moving along the

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Problem # B-5:

The position of an object moving along the

(a) Find the position of the object at

(b) What is the displacement of the object between

(c) What is the average velocity of the object between

(d) What is the average speed of the object between

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Problem # B-6:

The position of an object moving along the

(a) What is the average velocity of the object between 0 and

(b) What is the average speed of the object between 0 and

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Problem # B-7:

A delivery truck drives 6.5 km along a straight road. The driver then exits the truck, walks 1.5 km to deliver a package at one house, and then continues walking another 2 km to deliver a package to another house. The driver then walks back to the truck. The driving speed of the truck is 70 km/h, and the walking speed of the driver is 5 km/h.

(a) What is the average velocity and average speed of the driver from the start of the drive until the time that the package is delivered to the second house?

(b) What is the average velocity and average speed of the driver from the start of the drive until the time that the driver returns to the truck?

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Problem # B-8:

An object moves along the positive

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Problem # B-9:

An object moves along the positive

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Problem # C-1:

The position of a particle is given by

(a) What is the velocity of the particle at

(b) Is the position of the particle increasing or decreasing at

(c) What is the speed of the particle at

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Problem # C-2:

A particle's position is given by

(a) At what time is the velocity of the particle equal to -1.5 m/s ?

(b) At what time is the speed of the particle equal to 1.5 m/s ?

(c) What is the minimum velocity and minimum speed of the particle?

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Problem # D-1:

A particle's position is given by

(a) What is the average acceleraton of the particle between

(b) What is the acceleraton of the particle at

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Problem # D-2:

A particle is moving towards the right at 21 m/s, at a time of 3.1 s, and is moving towards the left at 18 m/s, at a time of 6.4 s. What is the average acceleration of the particle from 3.1 s to 6.4 s ?

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