Energy, work & power: AS Level Mathematics questions with answers
Free Energy, work & power questions for AS 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 24 kW. The resistance to motion is constant and equal to 600 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 = 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)
40 m s−1
driving force = resistance at maximum speed, P = Fv M1 40 A1
2
(b)
0.667 m s−2
driving force = 24000 ÷ 15 B1 F − R = ma M1 0.667 A1
3
(c)
24.6 m s−1
weight component 1500 × 10 ÷ 40 = 375 N B1 P ÷ v = R + mg sin θ M1 24.6 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 = 0.28. The coefficient of friction is 0.25.
(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)
48 J
R = 4 × 10 × 0.96 B1 F = 9.6 N M1 48 A1
3
(b)
3.61 m s−1
PE loss + initial KE = final KE + work against friction M1 correct equation A1 3.61 A1
3
Question 3Structured · 4 marks
A car of mass 1300 kg travels on a straight horizontal road against a resistance of 1400 N. The engine works at 20 kW. Find the acceleration when the speed is 28 m s−1.
[4]
Show answers and mark scheme
Part
Answer and marking points
Marks
−0.527 m s−2
Driving force = P ÷ v M1 714 N A1 F − R = ma M1 −0.527 A1
4
Question 4Structured · 4 marks
A child of mass 68 kg slides from rest down a slide of length 40 m. The bottom of the slide is 18 m below the top. The child reaches the bottom with speed 10 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
8840 J; 221 N
PE loss = mgh B1 work–energy M1 8840 A1 221 A1
4
Question 5Structured · 8 marksA* challenge
A car of mass 800 kg has an engine working at a constant power of 30 kW. The resistance to motion is constant and equal to 600 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 = 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)
50 m s−1
driving force = resistance at maximum speed, P = Fv M1 50 A1
2
(b)
1.75 m s−2
driving force = 30000 ÷ 15 B1 F − R = ma M1 1.75 A1
3
(c)
37.5 m s−1
weight component 800 × 10 ÷ 40 = 200 N B1 P ÷ v = R + mg sin θ M1 37.5 A1
3
Question 6Structured · 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 0.2.
(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)
76.8 J
R = 4 × 10 × 0.96 B1 F = 7.68 N M1 76.8 A1
3
(b)
4.65 m s−1
PE loss + initial KE = final KE + work against friction M1 correct equation A1 4.65 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