9709/41/M/J/25q4 – Mark Scheme

A lorry of mass 18,000kg is travelling along a straight road.

(a) On a horizontal section of the road, the power of the lorry’s engine is constant. There is a constant resistance to motion of 1600 N.

(i) The steady speed which the lorry can maintain with the engine working at power P W is 30 ms^-1. Find the value of P. [1 mark]

(ii) At an instant when the speed of the lorry is 16ms^-1, its engine is working at a power of 40kW. Find the acceleration of the lorry at this instant. [2 marks]

(b) When the lorry has a speed of 20ms^-1, it begins to ascend a section of road inclined at an angle to the horizontal. The engine now works at a power of 120kW. There is no change in the lorry’s speed as it ascends the hill. The constant resistance to motion remains 1600N.

Find the value of . [3 marks]

9709/42/M/J/25q1 – Mark Scheme

A crate is being pushed in a straight line along a horizontal surface by a force of magnitude 25N inclined at above the horizontal. The crate moves a distance of 12m in 8 seconds with constant speed.

(a) Find the constant speed of the crate. [1 mark]

(b) Find the work done by the 25N force. [2 marks]

(c) Find the power at which the 25N force is working. [1 mark]

9709/43/M/J/25q5 – Mark Scheme

A van of mass 2500 kg travelling at speed v ms^-1 experiences a resistance force of kv² N. The constant power of the van’s engine is 62.5kW.

(a) The steady speed that the van could maintain when moving along a straight horizontal road is 50ms^-1.

Show that k = 0.5, and find the acceleration of the van when its speed is 25ms^-1 on this straight horizontal road. [4 marks]

The van begins to ascend a hill inclined at an angle to the horizontal. The van travels along a line of greatest slope of the hill. The speed of the van at the start of the hill is 20ms^-1, and its acceleration is 5a ms^-2. Later, on the same hill, the speed of the van is 30ms^-1, and its acceleration is a ms^-2. The power of the van’s engine remains at 62.5kW, and the resistance force remains at 0.5v² N.

(b) Find the value of a and the value of . [5 marks]

9709/42/F/M/25q3 – Mark Scheme

An aeroplane is flying at a constant speed.

(a) The aeroplane is flying horizontally. The aeroplane’s engines are producing a constant power of 5500kW, and the aeroplane experiences a constant horizontal resistance force of 25kN.

Find the speed of the aeroplane. [2 marks]

(b) The aeroplane then ascends 300m in 50s, while maintaining the same speed. The resistance force is no longer constant, and the work done against the resistance force in ascending the 300m is 270 000kJ. The mass of the aeroplane is 60 000kg.
Find the average power of the aeroplane’s engines. [4 marks]

9709/41/O/N/24q7 – Mark Scheme

A car has mass 1200kg. When the car is travelling at a speed of v ms^-1, there is a resistive force of magnitude kv N. The maximum power of the car’s engine is 92.16kW.

(a) The car travels along a straight level road.

(i) The car has a greatest possible constant speed of 48ms^-1. Show that k = 40. [1 mark]

(ii) At an instant when its speed is 45ms^-1, find the greatest possible acceleration of the car. [3 marks]

(b) The car now travels at a constant speed up a hill inclined at an angle of sin^-10.15 to the horizontal.

Find the greatest possible speed of the car going up the hill. [4 marks]