Impulse Examples: 45 Problems with Answers

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

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 product of force and time interval, equal to the resulting change in an object's momentum.

A big push for a short time or a small push for a long time can have the same effect.

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: Impulse works by defining the interacting system and comparing motion before and after the interaction.

Common stuck point: Students often know a formula related to impulse but skip the recognition step: Is the interaction short, collision-like, or rotational, and have I checked whether external forces or torques can be ignored? That leads to a correct-looking substitution attached to the wrong physical model.

Sense of Study hint: Ask: Is the interaction short, collision-like, or rotational, and have I checked whether external forces or torques can be ignored?

Worked Examples

Example 1

easy

A force of

200 \text{ N}

acts on a ball for

0.05 \text{ s}

. What is the impulse delivered to the ball?

Answer

J = 10 N s

First step

Recall the impulse formula:

J = F \Delta t

, where

F

is the applied force and

\Delta t

is the time interval.

Full solution

2
Identify the given values: $F = 200 \text{ N}$ , $\Delta t = 0.05 \text{ s}$ .
3
Substitute and calculate: $J = 200 \times 0.05 = 10 N s$

Impulse is the product of force and the time interval over which it acts. It equals the change in momentum of the object.

Example 2

medium

0.15 \text{ kg}

baseball moving at

40 \text{ m/s}

is hit by a bat and reverses direction at

50 \text{ m/s}

. What impulse did the bat deliver?

Example 3

medium

0.5\text{ kg}

ball moving east at

4\text{ m/s}

rebounds west at

4\text{ m/s}

. Find the impulse on the ball.

Example 4

medium

0.5\text{ kg}

ball moving

6\text{ m/s}

east is hit and travels

8\text{ m/s}

north. Find the magnitude of the impulse.

Practice Problems

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

Example 1

medium

60 \text{ kg}

person jumps and lands on the ground, changing velocity from

-4 \text{ m/s}

(downward) to

0 \text{ m/s}

0.5 \text{ s}

. What average force does the ground exert?

Example 2

medium

0.20 \text{ kg}

hockey puck moves at

3 \text{ m/s}

east, then is struck and moves at

7 \text{ m/s}

west. What impulse was delivered to the puck?

Example 3

easy

5

N force acts on an object for

3

s. What impulse does it deliver?

Example 4

easy

An impulse of

12

\cdot

s acts on a

4

kg object initially at rest. Find its final velocity.

Example 5

easy

2

kg ball changes momentum by

10

\cdot

m/s. What impulse acted on it?

Example 6

easy

4

N force acts for

0.5

s. Find the impulse.

Example 7

easy

3

kg object speeds up from

2

m/s to

5

m/s. What impulse did it receive?

Example 8

easy

A constant

20

N force acts for

0.25

s on a ball. Find the impulse.

Example 9

easy

An impulse of

6

\cdot

s changes a

2

kg object's velocity. By how much does its velocity change?

Example 10

easy

A force-time graph shows a constant

8

N over

2

s. What is the impulse (area under the graph)?

Example 11

medium

0.5

kg ball hits a wall at

6

m/s and rebounds at

4

m/s. Find the impulse from the wall.

Example 12

medium

1500

kg car going

20

m/s stops in

5

s. Find the average braking force.

Example 13

medium

0.2

kg ball is hit, going from rest to

30

m/s during a

0.02

s contact. Find the average force.

Example 14

medium

The same

6

\cdot

m/s impulse is applied to a ball over

0.1

s instead of

0.02

s. Find the new average force.

Example 15

medium

2

kg object at

5

m/s experiences a

-3

\cdot

s impulse (opposite its motion). Find its new speed.

Example 16

medium

0.5

kg ball moving at

4

m/s east turns to

3

m/s north after a kick. Find the impulse magnitude.

Example 17

medium

A varying force gives a triangular force-time graph peaking at

10

N over

0.4

s (triangle from

0

0.4

s). Find the impulse.

Example 18

medium

70

kg person lands from a jump at

6

m/s and stops. Compare the force when stopping in

0.1

s vs

0.5

Example 19

medium

3

kg object at

4

m/s receives a

9

\cdot

s impulse in its direction of motion. Find its final speed.

Example 20

challenge

0.045

kg golf ball leaves the tee at

50

m/s after a

0.0005

s contact. Find the average force.

Example 21

challenge

2

kg ball falls and hits the ground at

10

m/s, rebounding at

8

m/s. If contact lasts

0.05

s, find the average force from the ground (

g=10

m/s

^2

Example 22

challenge

A machine gun fires

10

bullets per second, each

0.02

kg at

400

m/s. Find the average recoil force on the gun.

Example 23

easy

A constant

15\text{ N}

force pushes a cart for

0.4\text{ s}

. Find the impulse delivered.

Example 24

easy

2\text{ kg}

object's velocity changes from

3\text{ m/s}

7\text{ m/s}

. Find the impulse it received.

Example 25

easy

An impulse of

20\text{ N}\cdot\text{s}

acts on a

5\text{ kg}

object at rest. Find its final speed.

Example 26

easy

On a force-time graph, what physical quantity does the area under the curve represent?

Example 27

medium

0.06\text{ kg}

tennis ball travels at

30\text{ m/s}

, then is returned at

40\text{ m/s}

in the opposite direction. Find the impulse the racket gives the ball.

Example 28

medium

0.15\text{ kg}

ball gains

9\text{ m/s}

during a

0.03\text{ s}

contact. Find the average force exerted.

Example 29

medium

Why do airbags reduce the force on a driver in a crash, even though the change in momentum is the same?

Example 30

medium

A force-time graph is a triangle with peak

20\text{ N}

over

0.2\text{ s}

(base). Find the impulse.

Example 31

medium

1200\text{ kg}

car going

25\text{ m/s}

is brought to rest by brakes in

8\text{ s}

. Find the average braking force.

Example 32

medium

A force-time graph is rectangular at

50\text{ N}

from

t = 0.1\text{ s}

t = 0.5\text{ s}

. Find the impulse delivered.

Example 33

hard

0.045\text{ kg}

golf ball is struck and leaves at

70\text{ m/s}

after a

0.0008\text{ s}

contact. Find the average force.

Example 34

hard

0.05\text{ kg}

bullet exits a rifle at

400\text{ m/s}

. If the barrel acts on the bullet for

0.002\text{ s}

, what average force on the bullet? What impulse on the rifle?

Example 35

hard

0.5\text{ kg}

ball falls from

5\text{ m}

, hits the ground at

v = \sqrt{2gh}

, and rebounds at

80\%

of its impact speed. Find the impulse from the ground (

g=9.8

Example 36

hard

A garden hose ejects

5\text{ kg}

of water per second at

10\text{ m/s}

. Find the average reaction force on the nozzle.

Example 37

medium

4\text{ N}

force acts for

3\text{ s}

, then a

6\text{ N}

force in the opposite direction acts for

2\text{ s}

. Find the net impulse.

Example 38

challenge

50\text{ kg}

skydiver opens a parachute. Their velocity drops from

50\text{ m/s}

5\text{ m/s}

over

3\text{ s}

. Find the average force from the parachute (ignore gravity for impulse calc, then comment).

Example 39

medium

0.4\text{ kg}

ball has its velocity changed by

+5\text{ m/s}

. If you want to deliver this impulse in

0.5\text{ s}

instead of

0.1\text{ s}

, how does the average force change?

Example 40

medium

1\text{ kg}

object experiences forces of

5\text{ N}

for

2\text{ s}

followed by

-3\text{ N}

for

4\text{ s}

. Starting from rest, find its final velocity.

Example 41

challenge

A water jet of cross-section

A = 0.001\text{ m}^2

moving at

v = 20\text{ m/s}

hits a wall and stops dead. Find the force on the wall (

\rho = 1000\text{ kg/m}^3

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Related Concepts

Momentum Force Conservation of Momentum Collisions

Background Knowledge

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

momentumforce