Momentum: AS Level Mathematics questions with answers
Free Momentum questions for AS 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 2 kg, lie in that order in a straight line on a smooth horizontal surface. A is projected towards B with speed 8 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)
6 m s−1
2 × 8 = 2 × (−1) + 3v M1 6 A1
2
(b)
3.6 m s−1
momentum conserved for B and C M1 3.6 A1
2
(c)
30.6 J; no further collision because A moves away from the combined particle
KE before = ½ × 2 × 82M1 KE after for all particles M1 30.6 J A1 no further collision: A moves in the opposite direction B1
4
Question 2Structured · 5 marks
Particles P and Q of masses 0.3 kg and 0.5 kg move towards each other with speeds 6 m s−1 and 4 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
0.25 m s−1; 9.37 J
Conservation of momentum with signs M1 0.25 A1 KE before − KE after M1 Correct expressions A1 9.37 A1
5
Question 3Structured · 4 marks
A particle A of mass 0.5 kg moving at 7 m s−1 collides with a stationary particle B of mass 0.4 kg. After the collision A continues in the same direction at 1 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
7.5 m s−1; 0.75 J
conservation of momentum M1 7.5 A1 KE before − after M1 0.75 A1
4
Question 4Structured · 8 marksA* challenge
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 8 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)
6 m s−1
2 × 8 = 2 × (−1) + 3v M1 6 A1
2
(b)
4.5 m s−1
momentum conserved for B and C M1 4.5 A1
2
(c)
22.5 J; no further collision because A moves away from the combined particle
KE before = ½ × 2 × 82M1 KE after for all particles M1 22.5 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 0.6 kg move towards each other with speeds 5 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 m s−1; 9.6 J
Conservation of momentum with signs M1 1 A1 KE before − KE after M1 Correct expressions A1 9.6 A1
5
Question 6Structured · 4 marks
A particle A of mass 0.2 kg moving at 5 m s−1 collides with a stationary particle B of mass 0.8 kg. After the collision A continues in the same direction at 1 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
1 m s−1; 2 J
conservation of momentum M1 1 A1 KE before − after M1 2 A1
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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