Newton’s laws of motion: AS Level Mathematics questions with answers
Free Newton’s laws of motion questions for AS Level Mathematics (9709), part of Mechanics. Each question has the answer and the marking points an examiner would look for.
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, 1 m above the floor. The coefficient of friction between A and the table is 0.2. 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)
2 m s−2, 16 N
friction = 0.2 × 40 = 8 B1 Newton’s second law for A M1 Newton’s second law for B M1 a = 2 A1 T = 16 A1
5
(b)
2 m s−1
v2 = 2as M1 2 A1
2
(c)
2 m
deceleration of A = 2 m s−2B1 extra distance = 1 m M1 total 2 A1
3
Question 2Structured · 7 marksA* challenge
A car of mass 1500 kg tows a trailer of mass 500 kg along a straight horizontal road using a light rigid tow-bar. The resistances to motion are 300 N on the car and 100 N on the trailer.
(a)
The driving force of the car is 3000 N. Find the acceleration and the tension in the tow-bar.
[4]
(b)
The car is now braking with a braking force of 2000 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)
1.3 m s−2, 750 N
whole system equation M1 a = 1.3 A1 trailer equation M1 T = 750 A1
4
(b)
500 N, thrust
deceleration 1.2 B1 trailer equation M1 500 N thrust A1
3
Question 3Structured · 6 marks
A block of mass 2 kg is released from rest on a rough plane inclined at 35° to the horizontal. The coefficient of friction is 0.29. 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 = 3.36 m s−2, v = 4.49 m s−1
R = 2g cos 35 B1 F = μR M1 Newton II along plane M1 a = 3.36 A1 v2 = 2as M1 4.49 A1
6
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 7 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 = 5 m s−2; T = 35 N
friction = μ × 5g B1 Newton II for A M1 Newton II for B M1 a = 5 A1 T = 35 A1
5
Question 5Structured · 10 marksA* challenge
Particle A of mass 5 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, 1.2 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)
1.07 m s−2, 17.9 N
friction = 0.25 × 50 = 12.5 B1 Newton’s second law for A M1 Newton’s second law for B M1 a = 1.07 A1 T = 17.9 A1
5
(b)
1.6 m s−1
v2 = 2as M1 1.6 A1
2
(c)
1.71 m
deceleration of A = 2.5 m s−2B1 extra distance = 0.514 m M1 total 1.71 A1
3
Question 6Structured · 7 marksA* challenge
A car of mass 1800 kg tows a trailer of mass 500 kg along a straight horizontal road using a light rigid tow-bar. The resistances to motion are 300 N on the car and 100 N on the trailer.
(a)
The driving force of the car is 3600 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)
1.39 m s−2, 796 N
whole system equation M1 a = 1.39 A1 trailer equation M1 T = 796 A1
4
(b)
530 N, thrust
deceleration 1.26 B1 trailer equation M1 530 N thrust 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