Particle A, of mass 4 kg, moving at 5 m s−1, and particle B, of mass 2 kg, moving at 3 m s−1, move towards each other along a straight line. They collide and join together. Find their common speed.

v = 7/3 = 2.33 m s−1 (3 s.f.), in A's original direction.

Momentum and impulse practice problems Edexcel IAL Mechanics 1, Chapter 5

Written by STEM-Tutor's tutors · Updated October 2026 · 8 questions and 1 structured exam question

Momentum, impulse as change in momentum, and conservation of momentum in collisions between two particles, including particles that join together. Try each question before you look: use the hint if you are stuck, then reveal the worked solution one step at a time.

On this page

Key equations
Warm-up questions
Exam-style questions
Exam question practice
Common mistakes
Keep going

Key equations for momentum and impulse

p = mv	momentum (N s)
I = mv − mu	impulse = change in momentum
I = Ft	impulse of a constant force
m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂	conservation of momentum

Take g = 9.8 m s⁻², as the WME01 paper asks, and give answers to 2 or 3 significant figures. Answers within 2.5% are marked correct, so rounding along the way is fine. Revise the methods in our A level Maths mechanics guide.

Warm-up questions

Quick checks on the core ideas. If these feel easy, go straight to the exam-style questions.

Q1Warm-up

Find the momentum of a ball of mass 0.5 kg moving at 12 m s⁻¹.

Hint

p = mv.

Worked solution

p = 0.5 × 12 = 6 N s.

Q2Warm-up

A particle of mass 0.2 kg is at rest. It receives an impulse of 3 N s. Find its speed afterwards.

Hint

Impulse = change in momentum.

Worked solution

3 = 0.2v − 0.
v = 15 m s⁻¹.

Q3Warm-up

Which unit is used for impulse?

Hint

Impulse is force multiplied by time.

Worked solution

Force × time gives N s, the same as kg m s⁻¹: B.

Exam-style questions

Questions at the level of the Edexcel IAL Mechanics 1 exam. The ones marked Challenge combine more than one idea.

Q4Exam-style

Particle P, of mass 2 kg, moving at 6 m s⁻¹, hits particle Q, of mass 3 kg, which is at rest. After the collision P moves on in the same direction at 1.5 m s⁻¹. Find the speed of Q.

Hint

Momentum before = momentum after, with the direction of P's motion positive.

Worked solution

Before: 2 × 6 + 0 = 12. After: 2 × 1.5 + 3v = 3 + 3v.
12 = 3 + 3v.
v = 3 m s⁻¹.

Q5Exam-style

In the same collision, find the magnitude of the impulse exerted by P on Q.

Hint

Find the change in momentum of Q.

Worked solution

Impulse on Q = 3 × 3 − 3 × 0.
= 9 N s, equal and opposite to the impulse on P.

Q6Exam-style

A ball of mass 0.4 kg hits a vertical wall at 10 m s⁻¹ and rebounds along the same line at 6 m s⁻¹. Find the magnitude of the impulse on the ball.

Hint

The velocity changes direction, so one of them is negative.

Worked solution

Take the rebound direction as positive: u = −10, v = 6.
I = 0.4 × 6 − 0.4 × (−10) = 2.4 + 4.
I = 6.4 N s.

Q7Exam-style

Two particles collide on a smooth surface. Which statement is always true?

Hint

Think about Newton's third law during the collision.

Worked solution

The impulses on the two particles are equal and opposite, so the total momentum does not change.
Kinetic energy is usually lost. The answer is B.

Q8Challenge

Particle A, of mass 4 kg, moving at 5 m s⁻¹, and particle B, of mass 2 kg, moving at 3 m s⁻¹, move towards each other along a straight line. They collide and join together. Find their common speed.

Hint

B moves in the opposite direction, so its momentum is negative.

Worked solution

Take A's direction as positive. Before: 4 × 5 + 2 × (−3) = 14.
After: 6v = 14.
v = 7/3 = 2.33 m s⁻¹ (3 s.f.), in A's original direction.

Exam question practice

One original structured question in the style of the WME01 paper. Answer it in full, with working, before you open the mark scheme: M marks are for a correct method, A marks for accurate answers that follow from it, and B marks for a correct statement on its own.

Structured exam question style · 6 points · about 10 minutes

Two particles A and B move towards each other along the same straight line on a smooth horizontal surface. A has mass 2 kg and speed 5 m s⁻¹; B has mass m kg and speed 3 m s⁻¹. In the collision the direction of each particle is reversed. Immediately after, A has speed 1 m s⁻¹ and B has speed 2 m s⁻¹.

(a) Find the value of m.
(b) Find the magnitude of the impulse exerted on A in the collision.
(c) State what is meant by modelling the surface as smooth.

Write your full answer on paper first, then open the scoring guide and tick each point you earned.

Scoring guide and model answer

Part (a)

Taking A's original direction positive: 2(5) + m(−3) = 2(−1) + m(2). So 12 = 5m and m = 2.4.

1 point for: M1: conservation of momentum with the correct number of terms
1 point for: A1: correct signs throughout
1 point for: A1: m = 2.4

Part (b)

I = 2(−1) − 2(5) = −12, so the magnitude is 12 N s.

1 point for: M1: change in momentum of A, with a sign change
1 point for: A1: 12 N s

Part (c)

There is no friction between the particles and the surface.

1 point for: B1: no friction

Your mark: 0 of 6

Common mistakes in momentum and impulse

Leaving out the minus sign for a particle moving the other way. Draw a before-and-after diagram with arrows.
Giving a negative answer for a magnitude. Impulse magnitudes and speeds are positive.
Mixing up the impulse on A with the impulse on B: they are equal in size and opposite in direction.
Assuming kinetic energy is conserved. In M1 only momentum is.

Keep going

Revise the ideas behind these questions:

Then try real exam questions: Edexcel IAL Mechanics 1 past papers, with official scoring guidelines. · All Edexcel IAL Mechanics 1 units