AS Level Mathematics Paper 4 · Mechanics practice papers
50 marks · 1h 15m. Each generated paper follows the 9709 Paper 4 · Mechanics format, with the same number and style of questions as the real exam, and comes with a Cambridge-style mark scheme.
A particle P moves in a straight line, starting from rest at O. Its velocity at time t seconds after leaving O is v m s−1, where v = t2 − 4t + 3 for 0 ≤ t ≤ 5.
(a)
Find the acceleration of P at each instant when it is at instantaneous rest.
[3]
(b)
Find the displacement of P from O at t = 5.
[2]
(c)
Find the total distance travelled by P in the 5 seconds.
[4]
Show answers and mark scheme
Part
Answer and marking points
Marks
(a)
−2 m s−2 at t = 1; 2 m s−2 at t = 3
v = 0 solved M1 a = dvdt = 2t − 4 M1 both values A1
3
(b)
203 m
integrate v M1 203A1
2
(c)
283 m
split the interval at the times of rest M1 distances 43, 43, 203A1 sum of magnitudes M1 283A1
4
Question 2Structured · 6 marksA* challenge
A particle of mass 4 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 = 0.28. The coefficient of friction is 0.1.
(a)
Find the work done against friction as the particle moves 5 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)
19.2 J
R = 4 × 10 × 0.96 B1 F = 3.84 N M1 19.2 A1
3
(b)
4.73 m s−1
PE loss + initial KE = final KE + work against friction M1 correct equation A1 4.73 A1
3
Question 3Structured · 4 marks
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 2 m s−1. Find the speed of B after the collision and the loss of kinetic energy.
[4]
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Part
Answer and marking points
Marks
10 m s−1; 0 J
conservation of momentum M1 10 A1 KE before − after M1 0 A1
4
Question 4Structured · 5 marks
A block A of mass 5 kg lies on a rough horizontal table (coefficient of friction 0.2). It is connected by a light inextensible string over a smooth pulley at the edge to a particle B of mass 6 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 = 4.55 m s−2; T = 32.7 N
friction = μ × 5g B1 Newton II for A M1 Newton II for B M1 a = 4.55 A1 T = 32.7 A1
5
Question 5Structured · 4 marks
A car of mass 800 kg travels on a straight horizontal road against a resistance of 600 N. The engine works at 22 kW. Find the acceleration when the speed is 28 m s−1.
[4]
Show answers and mark scheme
Part
Answer and marking points
Marks
0.232 m s−2
Driving force = P ÷ v M1 786 N A1 F − R = ma M1 0.232 A1
4
Question 6Structured · 4 marks
A car accelerates uniformly from 7 m s−1 to 11 m s−1 in 10 s. Find (a) the acceleration, (b) the distance travelled in this time.
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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