Energy, work and power — AS & A Level Mathematics (9709) questions by topic
Working through a vertical cross-section slide with a curved and straight section, using an energy method on a particle projected up a smooth inclined plane, and analysing a cyclist's power, speed and acceleration on a flat road are typical of the 31 energy, work and power questions from 2023 to 2025, worth 3 to 11 marks.
Find, show and calculate are the three command words tracked here, each demanding an energy or work-done equation rather than a resolved-forces diagram. Because choosing energy methods over force methods, or vice versa, changes which quantities you need, submit your working for instant marking to catch a missed potential-energy term or a wrong power-force-velocity relationship as soon as it appears.
May–June 2025, Paper 41
A lorry of mass 18 000 kg is travelling along a straight road. On a horizontal section of the road, the power of the lorry's engine is constant. There is a constant resistance to…
Answer this question and get it marked →When a particle P of mass m kg has speed u m s^-1, its momentum is 4 N s and its kinetic energy is 16 J. Find the value of m and the value of u. [3]
Answer this question and get it marked →May–June 2025, Paper 42
A crate is being pushed in a straight line along a horizontal surface by a force of magnitude 25 N inclined at 20° above the horizontal. The crate moves a distance of 12 m in 8…
Answer this question and get it marked →A particle P of mass 3 kg is projected with a speed of 8 m s^-1 up a line of greatest slope of a rough plane inclined at 30° to the horizontal. P is projected from a point A on…
Answer this question and get it marked →May–June 2025, Paper 43
A van of mass 2500 kg travelling at speed v m s^-1 experiences a resistance force of k v^2 N. The constant power of the van's engine is 62.5 kW. The steady speed that the van…
Answer this question and get it marked →The diagram shows the vertical cross-section ABC of a rough waterslide. The section AB is a straight line of length 5 m inclined at an angle of theta to the horizontal, where…
Answer this question and get it marked →May–June 2025, Paper 45
A box of mass 25 kg is pulled 12 m up a rough plane inclined at an angle of 8 degrees to the horizontal. The box moves up a line of greatest slope against a frictional force of 50…
Answer this question and get it marked →A car of mass 1500 kg is travelling along a straight horizontal road. It is given that there is a constant resistance to motion. The engine of the car is working at 24 kW while…
Answer this question and get it marked →May–June 2024, Paper 41
A train of mass 180 000 kg ascends a straight hill of length 1.5 km, inclined at an angle of 1.5° to the horizontal. As it ascends the hill, the total work done to overcome the…
Answer this question and get it marked →A car of mass 1700 kg is pulling a trailer of mass 300 kg along a straight horizontal road. The car and trailer are connected by a light inextensible cable which is parallel to…
Answer this question and get it marked →May–June 2024, Paper 42
A cyclist and bicycle have a total mass of 72 kg. The cyclist rides along a horizontal road against a total resistance force of 28 N. Find the total work done by the cyclist to…
Answer this question and get it marked →A car has mass 1400 kg. When the speed of the car is v m s^-1 the magnitude of the resistance to motion is kv^2 N where k is a constant. The car moves at a constant speed of 24 m…
Answer this question and get it marked →May–June 2024, Paper 43
A cyclist is travelling along a straight horizontal road. The total mass of the cyclist and her bicycle is 80 kg. There is a constant resistance force of magnitude 32 N to the…
Answer this question and get it marked →The track ABCD lies in a vertical plane: AB is smooth and inclined at 30° to the horizontal, BC is rough and horizontal, and CD is rough and inclined at 30° to the horizontal,…
Answer this question and get it marked →October–November 2024, Paper 41
A particle of mass 7.5 kg, starting from rest at A, slides down an inclined plane AB. The point B is 12.5 metres vertically below the level of A, as shown in the diagram. Given…
Answer this question and get it marked →A car has mass 1200 kg. When the car is travelling at a speed of v m s^-1, there is a resistive force of magnitude kv N. The maximum power of the car's engine is 92.16 kW. (a) The…
Answer this question and get it marked →October–November 2024, Paper 42
A block of mass 20 kg is held at rest at the top of a plane inclined at 30° to the horizontal. The block is projected with speed 5 m s⁻¹ down a line of greatest slope of the…
Answer this question and get it marked →A cyclist is riding along a straight horizontal road. The total mass of the cyclist and his bicycle is 90 kg. The power exerted by the cyclist is 250 W. At an instant when the…
Answer this question and get it marked →October–November 2024, Paper 43
An athlete has mass m kg. The athlete runs along a horizontal road against a constant resistance force of magnitude 24 N. The total work done by the athlete in increasing his…
Answer this question and get it marked →A car of mass 1600 kg travels up a slope inclined at an angle of sin⁻¹0.08 to the horizontal, against a constant resistance of magnitude 240 N. It is given that the car travels at…
Answer this question and get it marked →Two particles, A and B, of masses 3 kg and 6 kg respectively, lie on a smooth horizontal plane. Initially B is at rest and A is moving towards B with speed 8 m s⁻¹. After A and B…
Answer this question and get it marked →May–June 2023, Paper 41
A car of mass 1200 kg is travelling along a straight horizontal road. The power of the car's engine is constant and is equal to 16 kW. There is a constant resistance to motion of…
Answer this question and get it marked →May–June 2023, Paper 42
A particle of mass 1.6 kg is dropped from a height of 9 m above horizontal ground. The speed of the particle at the instant before hitting the ground is 12 m s^-1. Find the work…
Answer this question and get it marked →An athlete of mass 84 kg is running along a straight road. Initially the road is horizontal and he runs at a constant speed of 3 m s^-1. The athlete produces a constant power of…
Answer this question and get it marked →May–June 2023, Paper 43
A lorry of mass 15 000 kg moves on a straight horizontal road from A to B, passing A and B with speeds 20 m s⁻¹ and 25 m s⁻¹ respectively. The engine's power is constant, the…
Answer this question and get it marked →The diagram shows the vertical cross-section XYZ of a rough slide. YZ is a straight line of length 2 m inclined at angle α to the horizontal, where sin α = 0.28, and is tangential…
Answer this question and get it marked →October–November 2023, Paper 41
A particle of mass 1.6 kg is projected with a speed of 20 m s^-1 up a line of greatest slope of a smooth plane inclined at α to the horizontal, where tan α = 3/4. Use an energy…
Answer this question and get it marked →A car of mass 1300 kg is moving on a straight road. On a horizontal section of the road, the car has a constant speed of 30 m s^-1 and there is a constant force of 650 N resisting…
Answer this question and get it marked →October–November 2023, Paper 42
A block of mass 15 kg slides down a line of greatest slope of an inclined plane. The top of the plane is at a vertical height of 1.6 m above the level of the bottom of the plane.…
Answer this question and get it marked →A block of mass 10 kg is at rest on a rough plane inclined at an angle of 30° to the horizontal. A force of 120 N is applied to the block at an angle of 20° above a line of…
Answer this question and get it marked →October–November 2023, Paper 43
A car has mass 1600 kg. The car is moving along a straight horizontal road at a constant speed of 24 m s^-1 and is subject to a constant resistance of magnitude 480 N. Find, in…
Answer this question and get it marked →Other AS & A Level Mathematics topics
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