Impulse Physics- Simple Problems Worksheet with Solutions

What Is Impulse in Physics?

Impulse is one of the most straightforward concepts in mechanics. It describes how a force applied over time changes an object's momentum. That's it. No metaphors, no complex philosophy.

The unit is Newton-seconds (N·s), which is equivalent to kg·m/s — the same as momentum units. This isn't a coincidence. The entire concept exists to explain the relationship between force, time, and motion change.

The Impulse-Momentum Theorem

This is the core equation you need:

J = FΔt = Δp = m(vf - vi)

Where:

• J = impulse (N·s)
• F = average force applied (N)
• Δt = time interval (s)
• m = mass (kg)
• vf = final velocity (m/s)
• vi = initial velocity (m/s)

The theorem states that impulse equals the change in momentum. You can calculate impulse either by looking at force × time, or by looking at the change in an object's momentum before and after the interaction.

Simple Problems with Solutions

Problem 1: Basic Impulse Calculation

A 2 kg ball rolling at 3 m/s is hit by a bat, changing its velocity to -8 m/s. The contact lasts 0.05 seconds. What average force was exerted?

Step 1: Find the change in momentum

Δp = m(vf - vi) = 2(-8 - 3) = 2(-11) = -22 kg·m/s

Step 2: Calculate force

F = Δp/Δt = -22/0.05 = -440 N

The negative sign indicates the force direction was opposite to the ball's original motion.

Problem 2: Finding Contact Time

A 0.5 kg tennis ball approaches a wall at 12 m/s and rebounds at 10 m/s. The wall exerts an average force of 200 N. How long was the contact?

Step 1: Calculate change in momentum

vf = -10 m/s (opposite direction), vi = 12 m/s

Δp = 0.5(-10 - 12) = 0.5(-22) = -11 kg·m/s

Step 2: Solve for time

Δt = Δp/F = -11/200 = 0.055 s

Problem 3: Car Crash Problem

A 1000 kg car traveling at 20 m/s crashes into a barrier and stops in 0.3 seconds. What average force acts on the car?

Step 1: Find impulse (change in momentum)

Δp = 1000(0 - 20) = -20,000 kg·m/s

Step 2: Calculate force

F = -20,000/0.3 = -66,667 N

That's roughly 6.8 tonnes of force. This is why crumple zones and airbags exist — they increase the time over which the momentum change occurs, reducing the average force.

How to Solve Any Impulse Problem

Follow this sequence every time:

1. Identify known variables — mass, initial velocity, final velocity, time, force. Write them down.
2. Determine what the problem is asking for — impulse, force, time, or velocity change.
3. Choose the right equation — J = FΔt for force/time problems, J = Δp = mΔv for momentum problems.
4. Watch your signs — velocity and force are vectors. Define a positive direction and stick to it.
5. Plug in numbers — double-check your arithmetic.
6. Include units — answers without units are incomplete.

Impulse vs. Momentum: The Difference

Students confuse these constantly. Here's the truth:

• Momentum (p) is a property of an object at a specific moment. It's mass × velocity.
• Impulse (J) is the process of changing that momentum. It's force × time.

Momentum tells you what's happening. Impulse tells you how it changed.

Quick Reference: Key Equations

Practice Problems (Try These Yourself)

1. A 3 kg object accelerates from rest to 15 m/s in 5 seconds. What impulse was applied?

2. A 0.1 kg bullet traveling at 400 m/s embeds into a wooden block and stops. If the average resisting force was 2000 N, how long did the penetration take?

3. A 50 kg person jumps from a platform onto concrete (stopping time ~0.01 s) versus into a foam pit (stopping time ~0.5 s). Calculate the average force for each scenario if they hit at 5 m/s.

Solutions to Practice Problems

Problem 1:

J = m(vf - vi) = 3(15 - 0) = 45 N·s

Problem 2:

Δp = 0.1(0 - 400) = -40 kg·m/s

Δt = Δp/F = -40/(-2000) = 0.02 s

Problem 3:

Δp = 50(0 - 5) = -250 kg·m/s

On concrete: F = -250/0.01 = -25,000 N

In foam pit: F = -250/0.5 = -500 N

The foam reduces impact force by 98%. That's why safety equipment works.

Common Mistakes to Avoid

• Forgetting to account for direction — if velocity changes sign, include the negative. Your impulse will be larger than expected if you ignore it.
• Mixing up initial and final velocity — always clarify which is which before plugging in.
• Using the wrong time interval — impulse problems often give you the contact time. Make sure you're using the actual collision duration, not something else.
• Dropping negative signs — negative impulse just means momentum decreased. That's often the whole point.

When Impulse Concepts Show Up

You'll encounter impulse in:

• Car crash analysis and safety engineering
• Sports science (batting, kicking, golf swings)
• Collision problems in conservation of momentum
• Material science (impact testing)
• Rocket propulsion and jet engines

The concept transfers directly to real-world engineering where you need to control how forces act during impacts.

Bottom Line

Impulse problems are algebraic. You have one main equation with five variables. Four out of five are usually given. Solve for the fifth. That's the entire process.

Once you can identify which variables you have and which you need, every impulse problem becomes routine.