Impulse Examples in Physics

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 N200 \text{ N} acts on a ball for 0.05 s0.05 \text{ s}. What is the impulse delivered to the ball?

Answer

J=10 N sJ = 10 \text{ N s}

First step

1
Recall the impulse formula: J=FΔtJ = F \Delta t, where FF is the applied force and Δt\Delta t is the time interval.

Full solution

  1. 2
    Identify the given values: F=200 NF = 200 \text{ N}, Δt=0.05 s\Delta t = 0.05 \text{ s}.
  2. 3
    Substitute and calculate: J=200×0.05=10 N sJ = 200 \times 0.05 = 10 \text{ 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
A 0.15 kg0.15 \text{ kg} baseball moving at 40 m/s40 \text{ m/s} is hit by a bat and reverses direction at 50 m/s50 \text{ m/s}. What impulse did the bat deliver?

Example 3

medium
A 0.5 kg0.5\text{ kg} ball moving east at 4 m/s4\text{ m/s} rebounds west at 4 m/s4\text{ m/s}. Find the impulse on the ball.

Example 4

medium
A 0.5 kg0.5\text{ kg} ball moving 6 m/s6\text{ m/s} east is hit and travels 8 m/s8\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
A 60 kg60 \text{ kg} person jumps and lands on the ground, changing velocity from −4 m/s-4 \text{ m/s} (downward) to 0 m/s0 \text{ m/s} in 0.5 s0.5 \text{ s}. What average force does the ground exert?

Example 2

medium
A 0.20 kg0.20 \text{ kg} hockey puck moves at 3 m/s3 \text{ m/s} east, then is struck and moves at 7 m/s7 \text{ m/s} west. What impulse was delivered to the puck?

Example 3

easy
A 55 N force acts on an object for 33 s. What impulse does it deliver?

Example 4

easy
An impulse of 1212 N⋅\cdots acts on a 44 kg object initially at rest. Find its final velocity.

Example 5

easy
A 22 kg ball changes momentum by 1010 kg⋅\cdotm/s. What impulse acted on it?

Example 6

easy
A 44 N force acts for 0.50.5 s. Find the impulse.

Example 7

easy
A 33 kg object speeds up from 22 m/s to 55 m/s. What impulse did it receive?

Example 8

easy
A constant 2020 N force acts for 0.250.25 s on a ball. Find the impulse.

Example 9

easy
An impulse of 66 N⋅\cdots changes a 22 kg object's velocity. By how much does its velocity change?

Example 10

easy
A force-time graph shows a constant 88 N over 22 s. What is the impulse (area under the graph)?

Example 11

medium
A 0.50.5 kg ball hits a wall at 66 m/s and rebounds at 44 m/s. Find the impulse from the wall.

Example 12

medium
A 15001500 kg car going 2020 m/s stops in 55 s. Find the average braking force.

Example 13

medium
A 0.20.2 kg ball is hit, going from rest to 3030 m/s during a 0.020.02 s contact. Find the average force.

Example 14

medium
The same 66 kg⋅\cdotm/s impulse is applied to a ball over 0.10.1 s instead of 0.020.02 s. Find the new average force.

Example 15

medium
A 22 kg object at 55 m/s experiences a −3-3 N⋅\cdots impulse (opposite its motion). Find its new speed.

Example 16

medium
A 0.50.5 kg ball moving at 44 m/s east turns to 33 m/s north after a kick. Find the impulse magnitude.

Example 17

medium
A varying force gives a triangular force-time graph peaking at 1010 N over 0.40.4 s (triangle from 00 to 0.40.4 s). Find the impulse.

Example 18

medium
A 7070 kg person lands from a jump at 66 m/s and stops. Compare the force when stopping in 0.10.1 s vs 0.50.5 s.

Example 19

medium
A 33 kg object at 44 m/s receives a 99 N⋅\cdots impulse in its direction of motion. Find its final speed.

Example 20

challenge
A 0.0450.045 kg golf ball leaves the tee at 5050 m/s after a 0.00050.0005 s contact. Find the average force.

Example 21

challenge
A 22 kg ball falls and hits the ground at 1010 m/s, rebounding at 88 m/s. If contact lasts 0.050.05 s, find the average force from the ground (g=10g=10 m/s2^2).

Example 22

challenge
A machine gun fires 1010 bullets per second, each 0.020.02 kg at 400400 m/s. Find the average recoil force on the gun.

Example 23

easy
A constant 15 N15\text{ N} force pushes a cart for 0.4 s0.4\text{ s}. Find the impulse delivered.

Example 24

easy
A 2 kg2\text{ kg} object's velocity changes from 3 m/s3\text{ m/s} to 7 m/s7\text{ m/s}. Find the impulse it received.

Example 25

easy
An impulse of 20 N⋅s20\text{ N}\cdot\text{s} acts on a 5 kg5\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
A 0.06 kg0.06\text{ kg} tennis ball travels at 30 m/s30\text{ m/s}, then is returned at 40 m/s40\text{ m/s} in the opposite direction. Find the impulse the racket gives the ball.

Example 28

medium
A 0.15 kg0.15\text{ kg} ball gains 9 m/s9\text{ m/s} during a 0.03 s0.03\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 N20\text{ N} over 0.2 s0.2\text{ s} (base). Find the impulse.

Example 31

medium
A 1200 kg1200\text{ kg} car going 25 m/s25\text{ m/s} is brought to rest by brakes in 8 s8\text{ s}. Find the average braking force.

Example 32

medium
A force-time graph is rectangular at 50 N50\text{ N} from t=0.1 st = 0.1\text{ s} to t=0.5 st = 0.5\text{ s}. Find the impulse delivered.

Example 33

hard
A 0.045 kg0.045\text{ kg} golf ball is struck and leaves at 70 m/s70\text{ m/s} after a 0.0008 s0.0008\text{ s} contact. Find the average force.

Example 34

hard
A 0.05 kg0.05\text{ kg} bullet exits a rifle at 400 m/s400\text{ m/s}. If the barrel acts on the bullet for 0.002 s0.002\text{ s}, what average force on the bullet? What impulse on the rifle?

Example 35

hard
A 0.5 kg0.5\text{ kg} ball falls from 5 m5\text{ m}, hits the ground at v=2ghv = \sqrt{2gh}, and rebounds at 80%80\% of its impact speed. Find the impulse from the ground (g=9.8g=9.8).

Example 36

hard
A garden hose ejects 5 kg5\text{ kg} of water per second at 10 m/s10\text{ m/s}. Find the average reaction force on the nozzle.

Example 37

medium
A 4 N4\text{ N} force acts for 3 s3\text{ s}, then a 6 N6\text{ N} force in the opposite direction acts for 2 s2\text{ s}. Find the net impulse.

Example 38

challenge
A 50 kg50\text{ kg} skydiver opens a parachute. Their velocity drops from 50 m/s50\text{ m/s} to 5 m/s5\text{ m/s} over 3 s3\text{ s}. Find the average force from the parachute (ignore gravity for impulse calc, then comment).

Example 39

medium
A 0.4 kg0.4\text{ kg} ball has its velocity changed by +5 m/s+5\text{ m/s}. If you want to deliver this impulse in 0.5 s0.5\text{ s} instead of 0.1 s0.1\text{ s}, how does the average force change?

Example 40

medium
A 1 kg1\text{ kg} object experiences forces of 5 N5\text{ N} for 2 s2\text{ s} followed by −3 N-3\text{ N} for 4 s4\text{ s}. Starting from rest, find its final velocity.

Example 41

challenge
A water jet of cross-section A=0.001 m2A = 0.001\text{ m}^2 moving at v=20 m/sv = 20\text{ m/s} hits a wall and stops dead. Find the force on the wall (ρ=1000 kg/m3\rho = 1000\text{ kg/m}^3).
← Back to Impulse Formula Explained Practice Mode

Background Knowledge

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

momentumforce