Momentum: A Level Mathematics questions with answers
Free Momentum questions for A Level Mathematics (9709), part of Mechanics. Each question has the answer and the marking points an examiner would look for.
Three particles A, B and C, of masses 2 kg, 3 kg and 1 kg, lie in that order in a straight line on a smooth horizontal surface. A is projected towards B with speed 5 m s−1; B and C are at rest. After A collides with B, A moves with speed 1 m s−1 in the opposite direction.
(a)
Find the speed of B immediately after the collision.
[2]
(b)
B then collides with C and the two particles coalesce. Find their common speed.
[2]
(c)
Find the total loss of kinetic energy in the two collisions, and state whether there is any further collision. Give a reason.
[4]
Show answers and mark scheme
Part
Answer and marking points
Marks
(a)
4 m s−1
2 × 5 = 2 × (−1) + 3v M1 4 A1
2
(b)
3 m s−1
momentum conserved for B and C M1 3 A1
2
(c)
6 J; no further collision because A moves away from the combined particle
KE before = ½ × 2 × 52M1 KE after for all particles M1 6 J A1 no further collision: A moves in the opposite direction B1
4
Question 2Structured · 5 marks
Particles P and Q of masses 0.5 kg and 0.6 kg move towards each other with speeds 7 m s−1 and 1 m s−1. They coalesce on impact. Find the speed of the combined particle and the loss of kinetic energy.
[5]
Show answers and mark scheme
Part
Answer and marking points
Marks
2.64 m s−1; 8.73 J
Conservation of momentum with signs M1 2.64 A1 KE before − KE after M1 Correct expressions A1 8.73 A1
5
Question 3Structured · 4 marks
A particle A of mass 0.2 kg moving at 8 m s−1 collides with a stationary particle B of mass 0.6 kg. After the collision A continues in the same direction at 2 m s−1. Find the speed of B after the collision and the loss of kinetic energy.
[4]
Show answers and mark scheme
Part
Answer and marking points
Marks
2 m s−1; 4.8 J
conservation of momentum M1 2 A1 KE before − after M1 4.8 A1
4
Question 4Structured · 8 marksA* challenge
Three particles A, B and C, of masses 2 kg, 3 kg and 2 kg, lie in that order in a straight line on a smooth horizontal surface. A is projected towards B with speed 5 m s−1; B and C are at rest. After A collides with B, A moves with speed 1 m s−1 in the opposite direction.
(a)
Find the speed of B immediately after the collision.
[2]
(b)
B then collides with C and the two particles coalesce. Find their common speed.
[2]
(c)
Find the total loss of kinetic energy in the two collisions, and state whether there is any further collision. Give a reason.
[4]
Show answers and mark scheme
Part
Answer and marking points
Marks
(a)
4 m s−1
2 × 5 = 2 × (−1) + 3v M1 4 A1
2
(b)
2.4 m s−1
momentum conserved for B and C M1 2.4 A1
2
(c)
9.6 J; no further collision because A moves away from the combined particle
KE before = ½ × 2 × 52M1 KE after for all particles M1 9.6 J A1 no further collision: A moves in the opposite direction B1
4
Question 5Structured · 5 marks
Particles P and Q of masses 0.6 kg and 0.4 kg move towards each other with speeds 4 m s−1 and 3 m s−1. They coalesce on impact. Find the speed of the combined particle and the loss of kinetic energy.
[5]
Show answers and mark scheme
Part
Answer and marking points
Marks
1.2 m s−1; 5.88 J
Conservation of momentum with signs M1 1.2 A1 KE before − KE after M1 Correct expressions A1 5.88 A1
5
Question 6Structured · 4 marks
A particle A of mass 0.4 kg moving at 6 m s−1 collides with a stationary particle B of mass 0.4 kg. After the collision A continues in the same direction at 3 m s−1. Find the speed of B after the collision and the loss of kinetic energy.
[4]
Show answers and mark scheme
Part
Answer and marking points
Marks
3 m s−1; 3.6 J
conservation of momentum M1 3 A1 KE before − after M1 3.6 A1
Riyaz Shaikh has mentored IGCSE, IB and A Level students for 15+ years, one-on-one, online and in Mumbai. The hardest questions on this site are the ones he uses to find a student's weak points.
Original Cambridge-style practice questions written for mentorriyaz.in. These are not Cambridge past paper questions, and this site is not affiliated with or endorsed by Cambridge University Press & Assessment. Updated 2026-11-04. Paper generator · mentorriyaz.in