Mechanics: AS Level Mathematics questions and answers
10 free AS 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.
A particle of mass 5 kg is projected with speed 2 m s−1 down a line of greatest slope of a rough plane inclined at α to the horizontal, where sin α = 0.6. The coefficient of friction is 0.2.
(a)
Find the work done against friction as the particle moves 10 m down the plane.
[3]
(b)
Use an energy method to find the speed of the particle after it has moved this distance.
[3]
Show answers and mark scheme
Part
Answer and marking points
Marks
(a)
80 J
R = 5 × 10 × 0.8 B1 F = 8 N M1 80 A1
3
(b)
9.59 m s−1
PE loss + initial KE = final KE + work against friction M1 correct equation A1 9.59 A1
3
Question 2Structured · 8 marksA* challenge
A car of mass 800 kg has an engine working at a constant power of 36 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 15 m s−1.
[3]
(c)
The car now travels up a hill inclined at angle θ to the horizontal, where sin θ = 120. 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)
45 m s−1
driving force = resistance at maximum speed, P = Fv M1 45 A1
2
(b)
2 m s−2
driving force = 36000 ÷ 15 B1 F − R = ma M1 2 A1
3
(c)
30 m s−1
weight component 800 × 10 ÷ 20 = 400 N B1 P ÷ v = R + mg sin θ M1 30 A1
3
Question 3Structured · 10 marksA* challenge
Particle A of mass 4 kg lies on a rough horizontal table. It is attached to a light inextensible string that passes over a smooth pulley at the edge of the table. Particle B of mass 2 kg hangs from the other end, 0.5 m above the floor. The coefficient of friction between A and the table is 0.25. The system is released from rest with the string taut. A does not reach the pulley.
(a)
Find the acceleration of the system and the tension in the string.
[5]
(b)
Find the speed of B when it hits the floor.
[2]
(c)
B does not rebound. Find the total distance moved by A before it comes to rest.
[3]
Show answers and mark scheme
Part
Answer and marking points
Marks
(a)
1.67 m s−2, 16.7 N
friction = 0.25 × 40 = 10 B1 Newton’s second law for A M1 Newton’s second law for B M1 a = 1.67 A1 T = 16.7 A1
5
(b)
1.29 m s−1
v2 = 2as M1 1.29 A1
2
(c)
0.833 m
deceleration of A = 2.5 m s−2B1 extra distance = 0.333 m M1 total 0.833 A1
3
Question 4Structured · 7 marksA* challenge
(a)
Particle A is projected vertically upwards from ground level with speed 20 m s−1. At the same instant particle B is projected vertically downwards with speed 10 m s−1 from a point 30 m directly above A. Find the time at which the particles meet and their height above the ground.
[5]
(b)
Find the velocity of each particle at the instant they meet.
[2]
Show answers and mark scheme
Part
Answer and marking points
Marks
(a)
1 s, 15 m
sA = 20t − 5t2B1 sB = 10t + 5t2B1 sA + sB = 30 M1 t = 1 A1 height 15 A1
5
(b)
A 10 m s−1 upwards, B 20 m s−1 downwards
v = u + at for each M1 both correct with directions A1
2
Question 5Structured · 5 marks
A block A of mass 5 kg lies on a rough horizontal table (coefficient of friction 0.1). It is connected by a light inextensible string over a smooth pulley at the edge to a particle B of mass 5 kg hanging freely. The system is released from rest. Find the acceleration and the tension in the string.
[5]
Show answers and mark scheme
Part
Answer and marking points
Marks
a = 4.5 m s−2; T = 27.5 N
friction = μ × 5g B1 Newton II for A M1 Newton II for B M1 a = 4.5 A1 T = 27.5 A1
5
Question 6Structured · 4 marks
A car accelerates uniformly from 4 m s−1 to 8 m s−1 in 4 s. Find (a) the acceleration, (b) the distance travelled in this time.
[4]
Show answers and mark scheme
Part
Answer and marking points
Marks
(a) 1 m s−2 (b) 24 m
v = u + at M1 1 A1 s = ½(u + v)t M1 24 A1
4
Question 7Structured · 5 marks
Particles P and Q of masses 0.3 kg and 0.6 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
0 m s−1; 8.1 J
Conservation of momentum with signs M1 0 A1 KE before − KE after M1 Correct expressions A1 8.1 A1
5
Question 8Structured · 5 marks
A particle of weight 51 N hangs in equilibrium from two strings. The strings make angles of 40° and 60° with the horizontal. Find the tensions in the strings.
A particle A of mass 0.5 kg moving at 8 m s−1 collides with a stationary particle B of mass 0.3 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
8.33 m s−1; 3.33 J
conservation of momentum M1 8.33 A1 KE before − after M1 3.33 A1
4
Question 10Structured · 5 marks
A particle starts from rest at O and moves in a straight line with acceleration a = (8 − 2t) m s−2.
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