Mechanics: A Level Mathematics questions and answers
10 free A Level Mathematics Mechanics questions written in the style of Cambridge Mathematics papers, each with its answer and mark scheme. 4 of them are A* challenge questions, built to catch the mistakes strong students still make.
This topic covers Forces & equilibrium, Kinematics in a straight line, Momentum, Newton’s laws of motion, Energy, work & power. Work through the questions below, then generate a full Mechanics paper with a fresh set every time.
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 marksA* challenge
A particle is in equilibrium under three forces: its weight of 9 N, a horizontal force of 10 N, and a force of P N acting at an angle α above the horizontal. Find P and α.
[5]
Show answers and mark scheme
Part
Answer and marking points
Marks
P = 13.5, α = 42.0°
resolve horizontally: P cos α = 10 M1 resolve vertically: P sin α = 9 M1 tan α = 910M1 α = 42.0° A1 P = 13.5 A1
5
Question 3Structured · 7 marksA* challenge
A car of mass 1200 kg tows a trailer of mass 400 kg along a straight horizontal road using a light rigid tow-bar. The resistances to motion are 500 N on the car and 200 N on the trailer.
(a)
The driving force of the car is 2500 N. Find the acceleration and the tension in the tow-bar.
[4]
(b)
The car is now braking with a braking force of 2500 N and no driving force. Find the force in the tow-bar and state whether it is a tension or a thrust.
[3]
Show answers and mark scheme
Part
Answer and marking points
Marks
(a)
1.13 m s−2, 650 N
whole system equation M1 a = 1.13 A1 trailer equation M1 T = 650 A1
4
(b)
600 N, thrust
deceleration 2 B1 trailer equation M1 600 N thrust A1
3
Question 4Structured · 8 marksA* challenge
A car of mass 1200 kg has an engine working at a constant power of 30 kW. The resistance to motion is constant and equal to 800 N.
(a)
Find the greatest possible speed of the car on a straight horizontal road.
[2]
(b)
Find the acceleration of the car on the horizontal road when its speed is 12 m s−1.
[3]
(c)
The car now travels up a hill inclined at angle θ to the horizontal, where sin θ = 125. The power and the resistance are unchanged. Find the greatest possible speed of the car up the hill.
[3]
Show answers and mark scheme
Part
Answer and marking points
Marks
(a)
37.5 m s−1
driving force = resistance at maximum speed, P = Fv M1 37.5 A1
2
(b)
1.42 m s−2
driving force = 30000 ÷ 12 B1 F − R = ma M1 1.42 A1
3
(c)
23.4 m s−1
weight component 1200 × 10 ÷ 25 = 480 N B1 P ÷ v = R + mg sin θ M1 23.4 A1
3
Question 5Structured · 5 marks
A particle starts from rest at O and moves in a straight line with acceleration a = (4 − 2t) m s−2.
(a)
Find the velocity when the acceleration is zero.
[3]
(b)
Find the displacement from O at this time.
[2]
Show answers and mark scheme
Part
Answer and marking points
Marks
(a)
4 m s−1
integrate a M1 v = 4t − t2A1 t = 2: v = 4 A1
3
(b)
163 m
integrate v M1 163A1
2
Question 6Structured · 4 marks
A child of mass 57 kg slides from rest down a slide of length 42 m. The bottom of the slide is 18 m below the top. The child reaches the bottom with speed 4 m s−1. Find the work done against resistance and the average resistance force.
[4]
Show answers and mark scheme
Part
Answer and marking points
Marks
9800 J; 233 N
PE loss = mgh B1 work–energy M1 9800 A1 233 A1
4
Question 7Structured · 4 marks
A car of mass 900 kg travels on a straight horizontal road against a resistance of 1000 N. The engine works at 48 kW. Find the acceleration when the speed is 30 m s−1.
[4]
Show answers and mark scheme
Part
Answer and marking points
Marks
0.667 m s−2
Driving force = P ÷ v M1 1600 N A1 F − R = ma M1 0.667 A1
4
Question 8Structured · 6 marks
A particle moves in a straight line. Its velocity t seconds after leaving O is v = 3t(4 − t) m s−1 for 0 ≤ t ≤ 4.
(a)
Find the maximum velocity.
[3]
(b)
Find the distance travelled in the 4 seconds.
[3]
Show answers and mark scheme
Part
Answer and marking points
Marks
(a)
12 m s−1
dvdt = 0 M1 t = 2 A1 12 A1
3
(b)
32 m
integrate M1 limits 0 to 4 M1 32 A1
3
Question 9Structured · 6 marks
A block of mass 10 kg is released from rest on a rough plane inclined at 25° to the horizontal. The coefficient of friction is 0.39. Find the acceleration of the block and its speed after it has moved 3 m. [Use g = 10 m s−2]
[6]
Show answers and mark scheme
Part
Answer and marking points
Marks
a = 0.692 m s−2, v = 2.04 m s−1
R = 10g cos 25 B1 F = μR M1 Newton II along plane M1 a = 0.692 A1 v2 = 2as M1 2.04 A1
6
Question 10Structured · 5 marks
Particles P and Q of masses 0.5 kg and 0.5 kg move towards each other with speeds 6 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
1.5 m s−1; 10.1 J
Conservation of momentum with signs M1 1.5 A1 KE before − KE after M1 Correct expressions A1 10.1 A1
In the 9709 syllabus, Mechanics covers Forces & equilibrium, Kinematics in a straight line, Momentum, Newton’s laws of motion, Energy, work & power.
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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