Energy, work & power: A Level Mathematics questions with answers
Free Energy, work & power questions for A Level Mathematics (9709), part of Mechanics. Each question has the answer and the marking points an examiner would look for.
A car of mass 1500 kg has an engine working at a constant power of 40 kW. The resistance to motion is constant and equal to 500 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 10 m s−1.
[3]
(c)
The car now travels up a hill inclined at angle θ to the horizontal, where sin θ = 140. 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)
80 m s−1
driving force = resistance at maximum speed, P = Fv M1 80 A1
2
(b)
2.33 m s−2
driving force = 40000 ÷ 10 B1 F − R = ma M1 2.33 A1
3
(c)
45.7 m s−1
weight component 1500 × 10 ÷ 40 = 375 N B1 P ÷ v = R + mg sin θ M1 45.7 A1
3
Question 2Structured · 6 marksA* challenge
A particle of mass 4 kg is projected with speed 3 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 0.25.
(a)
Find the work done against friction as the particle moves 8 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)
64 J
R = 4 × 10 × 0.8 B1 F = 8 N M1 64 A1
3
(b)
8.54 m s−1
PE loss + initial KE = final KE + work against friction M1 correct equation A1 8.54 A1
3
Question 3Structured · 4 marks
A car of mass 900 kg travels on a straight horizontal road against a resistance of 1500 N. The engine works at 39 kW. Find the acceleration when the speed is 21 m s−1.
[4]
Show answers and mark scheme
Part
Answer and marking points
Marks
0.397 m s−2
Driving force = P ÷ v M1 1860 N A1 F − R = ma M1 0.397 A1
4
Question 4Structured · 4 marks
A child of mass 72 kg slides from rest down a slide of length 51 m. The bottom of the slide is 10 m below the top. The child reaches the bottom with speed 8 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
4900 J; 96 N
PE loss = mgh B1 work–energy M1 4900 A1 96 A1
4
Question 5Structured · 8 marksA* challenge
A car of mass 1000 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 10 m s−1.
[3]
(c)
The car now travels up a hill inclined at angle θ to the horizontal, where sin θ = 140. 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)
2.8 m s−2
driving force = 36000 ÷ 10 B1 F − R = ma M1 2.8 A1
3
(c)
34.3 m s−1
weight component 1000 × 10 ÷ 40 = 250 N B1 P ÷ v = R + mg sin θ M1 34.3 A1
3
Question 6Structured · 6 marksA* challenge
A particle of mass 8 kg is projected with speed 4 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 0.1.
(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)
64 J
R = 8 × 10 × 0.8 B1 F = 6.4 N M1 64 A1
3
(b)
11 m s−1
PE loss + initial KE = final KE + work against friction M1 correct equation A1 11 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