Kinetic Energy Examples: 47 Problems with Answers

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Kinetic Energy.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Physics.

Concept Recap

The energy an object possesses by virtue of its motion, equal to one-half times its mass times the square of its velocity.

The faster something moves and the heavier it is, the more kinetic energy it has.

Read the full concept explanation →

How to Use These Examples

Read the first worked example with the solution open so the structure is clear.
Try the practice problems before revealing each solution.
Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Kinetic Energy asks what energy enters, leaves, stays stored, or changes form in the chosen system.

Common stuck point: Students often know a formula related to kinetic energy but skip the recognition step: Can I define the system and track energy before and after the interaction or process? That leads to a correct-looking substitution attached to the wrong physical model.

Sense of Study hint: Ask: Can I define the system and track energy before and after the interaction or process?

Worked Examples

Example 1

easy

What is the kinetic energy of a

3 \text{ kg}

ball moving at

8 \text{ m/s}

Answer

K E = 96 J

First step

Use the kinetic energy formula:

KE = \frac{1}{2}mv^2

Full solution

2
Square the speed first: $8^2 = 64$ .
3
$K E = \frac{1}{2} (3) (64) = 96 J$

Kinetic energy is the energy of motion. It depends on both mass and velocity, but velocity has a squared relationship, so doubling speed quadruples KE.

Example 2

medium

A car doubles its speed from

15 \text{ m/s}

30 \text{ m/s}

. By what factor does its kinetic energy change?

Example 3

medium

1200\text{ kg}

car accelerates from

10\text{ m/s}

25\text{ m/s}

. How much work was done on it (assuming no losses)?

Example 4

medium

2\text{ kg}

object's speed increases from

3\text{ m/s}

7\text{ m/s}

. How much energy was added?

Example 5

hard

0.1\text{ kg}

ball moving east at

4\text{ m/s}

collides head-on with a

0.2\text{ kg}

ball moving west at

2\text{ m/s}

. After the collision they stick together. Find the kinetic energy lost in the collision.

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

medium

0.5 \text{ kg}

ball has

100 \text{ J}

of kinetic energy. What is its speed?

Example 2

easy

1200 \text{ kg}

car doubles its speed from

15 \text{ m/s}

30 \text{ m/s}

. By what factor does its kinetic energy increase?

Example 3

easy

A 2 kg object moves at 3 m/s. Find its kinetic energy.

Example 4

easy

A 4 kg object moves at 5 m/s. What is its kinetic energy?

Example 5

easy

Can kinetic energy be negative?

Example 6

easy

If speed doubles, by what factor does kinetic energy change?

Example 7

easy

A 10 kg object has KE = 80 J. What is its speed?

Example 8

easy

Two objects, 2 kg and 6 kg, both move at 3 m/s. Which has more kinetic energy?

Example 9

easy

A 1 kg ball at rest. What is its kinetic energy?

Example 10

easy

Is kinetic energy a vector or a scalar?

Example 11

medium

A 1500 kg car travels at 20 m/s. Find its kinetic energy.

Example 12

medium

A 3 kg object speeds up from 2 m/s to 4 m/s. Find the change in kinetic energy.

Example 13

medium

A bullet (0.02 kg) and a runner (60 kg) both have KE = 100 J. Which moves faster, and what is the bullet's speed?

Example 14

medium

A 0.5 kg ball moving at 6 m/s is brought to rest. How much energy must be removed?

Example 15

medium

An object's KE increases from 20 J to 45 J while mass stays constant. By what factor did its speed increase?

Example 16

medium

A 2 kg object has horizontal speed 3 m/s and vertical speed 4 m/s. Find its kinetic energy.

Example 17

medium

A 5 kg object loses 60 J of KE, slowing from some speed to 2 m/s. What was its initial speed?

Example 18

challenge

A 1000 kg car at 30 m/s and a 2000 kg truck at 15 m/s. Which has more kinetic energy, and what is the ratio car:truck?

Example 19

challenge

A 0.145 kg baseball is thrown at 40 m/s. If a catcher's glove stops it over 0.1 m, what average force is needed (use KE and work)?

Example 20

challenge

A proton and an alpha particle (mass 4 times the proton) have equal kinetic energy. Find the ratio of their speeds (proton:alpha).

Example 21

medium

A 0.05 kg bullet at 400 m/s. Find its kinetic energy.

Example 22

medium

A 2 kg object's KE doubles from 16 J. What is its new speed?

Example 23

easy

6\text{ kg}

box slides at

2\text{ m/s}

. Find its kinetic energy.

Example 24

easy

8\text{ kg}

object moves at

5\text{ m/s}

. Find its kinetic energy.

Example 25

easy

0.5\text{ kg}

ball has kinetic energy

36\text{ J}

. Find its speed.

Example 26

easy

0.2\text{ kg}

apple falls and just before hitting the ground has

KE = 4\text{ J}

. Find its speed at that instant.

Example 27

medium

0.04\text{ kg}

arrow leaves a bow with

KE = 50\text{ J}

. Find its launch speed.

Example 28

medium

0.5\text{ kg}

ball has horizontal velocity

6\text{ m/s}

and vertical velocity

8\text{ m/s}

. Find its kinetic energy.

Example 29

medium

A net force of

20\text{ N}

acts on a

4\text{ kg}

object over a distance of

5\text{ m}

. If the object started at rest, find its final speed.

Example 30

medium

A roller coaster car (

500\text{ kg}

) descends a

20\text{ m}

hill from rest. Ignoring friction and using

g = 9.8\text{ m/s}^2

, find its kinetic energy at the bottom.

Example 31

medium

A truck (mass

M

) and a car (mass

M/2

) have the same kinetic energy. Find the ratio of their speeds

v_{\text{car}}/v_{\text{truck}}

Example 32

medium

0.45\text{ kg}

soccer ball is kicked at

20\text{ m/s}

. Find its kinetic energy.

Example 33

medium

1500\text{ kg}

car traveling at

20\text{ m/s}

brakes to a stop. How much energy is dissipated by the brakes (assume all KE becomes heat)?

Example 34

hard

50\text{ kg}

skier starts from rest at the top of a

15\text{ m}

frictionless slope. Find her kinetic energy and speed at the bottom (use

g = 9.8\text{ m/s}^2

Example 35

hard

An electron (

m = 9.11\times10^{-31}\text{ kg}

) is accelerated from rest through a potential difference of

100\text{ V}

. Find its kinetic energy in joules and its final speed.

Example 36

hard

2\text{ kg}

block slides on a horizontal surface with friction coefficient

\mu_k = 0.3

. It starts at

5\text{ m/s}

. How far does it travel before stopping (use

g = 9.8\text{ m/s}^2

Example 37

hard

0.3\text{ kg}

mass on a spring oscillates. At maximum displacement (amplitude),

PE = 12\text{ J}

and

KE = 0

. Find the kinetic energy at the equilibrium position (assume no friction).

Example 38

hard

Express kinetic energy in terms of momentum

p

and mass

m

Example 39

hard

Two objects have the same momentum

p

. Object A has mass

m

, object B has mass

4m

. Find the ratio of kinetic energies

KE_A/KE_B

Example 40

challenge

0.02\text{ kg}

bullet at

300\text{ m/s}

embeds itself in a

2\text{ kg}

block at rest on a frictionless surface. Find the kinetic energy lost to deformation and heat.

Example 41

challenge

200\text{ g}

pendulum bob swings down from rest at a height

h

above its lowest point. At the bottom its speed is

4\text{ m/s}

. Find

h

(use

g = 9.8\text{ m/s}^2

Example 42

challenge

Total kinetic energy of a hoop (mass

m

, radius

R

) rolling without slipping at speed

v

KE = \tfrac{1}{2}mv^2 + \tfrac{1}{2}I\omega^2

with

I = mR^2

. Find the total kinetic energy as a multiple of

\tfrac{1}{2}mv^2

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Related Concepts

Energy Velocity Mass Work-Energy Theorem Momentum

Background Knowledge

These ideas may be useful before you work through the harder examples.

energyvelocitymass