Instantaneous change in power or force

A question is this type if and only if the power or driving force is suddenly increased or decreased and you must find the instantaneous acceleration or deceleration immediately after the change, at the same speed.

9 questions · Moderate -0.1

6.02l Power and velocity: P = Fv
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CAIE M1 2021 November Q4
9 marks Moderate -0.3
4 A car of mass 1400 kg is moving on a straight road against a constant force of 1250 N resisting the motion.
  1. The car moves along a horizontal section of the road at a constant speed of \(36 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).
    1. Calculate the work done against the resisting force during the first 8 seconds.
    2. Calculate, in kW , the power developed by the engine of the car.
    3. Given that this power is suddenly increased by 12 kW , find the instantaneous acceleration of the car.
  2. The car now travels at a constant speed of \(32 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) up a section of the road inclined at \(\theta ^ { \circ }\) to the horizontal, with the engine working at 64 kW . Find the value of \(\theta\).
CAIE M1 2016 June Q6
8 marks Moderate -0.8
6 A car of mass 1100 kg is moving on a road against a constant force of 1550 N resisting the motion.
  1. The car moves along a straight horizontal road at a constant speed of \(40 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).
    1. Calculate, in kW , the power developed by the engine of the car.
    2. Given that this power is suddenly decreased by 22 kW , find the instantaneous deceleration of the car.
    3. The car now travels at constant speed up a straight road inclined at \(8 ^ { \circ }\) to the horizontal, with the engine working at 80 kW . Assuming the resistance force remains the same, find this constant speed.
Edexcel M2 2018 Specimen Q1
8 marks Standard +0.2
  1. A car of mass 900 kg is travelling up a straight road inclined at an angle \(\theta\) to the horizontal, where \(\sin \theta = \frac { 1 } { 25 }\). The car is travelling at a constant speed of \(14 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and the resistance to motion from non-gravitational forces has a constant magnitude of 800 N . The car takes 10 seconds to travel from \(A\) to \(B\), where \(A\) and \(B\) are two points on the road.
    1. Find the work done by the engine of the car as the car travels from \(A\) to \(B\).
    When the car is at \(B\) and travelling at a speed of \(14 \mathrm {~ms} ^ { - 1 }\) the rate of working of the engine of the car is suddenly increased to \(P \mathrm {~kW}\), resulting in an initial acceleration of the car of \(0.7 \mathrm {~m} \mathrm {~s} ^ { - 2 }\). The resistance to motion from non-gravitational forces still has a constant magnitude of 800 N .
  2. Find the value of \(P\).
    □
Edexcel M2 Specimen Q4
8 marks Moderate -0.3
4. A car of mass 750 kg is moving up a straight road inclined at an angle \(\theta\) to the horizontal, where \(\sin \theta = \frac { 1 } { 15 }\). The resistance to motion of the car from non-gravitational forces has constant magnitude R newtons. The power developed by the car's engine is 15 kW and the car is moving at a constant speed of \(20 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).
  1. Show that \(\mathrm { R } = 260\). The power developed by the car's engine is now increased to 18 kW . The magnitude of the resistance to motion from non-gravitational forces remains at 260 N . At the instant when the car is moving up the road at \(20 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) the car's acceleration is a \(\mathrm { m } \mathrm { s } ^ { - 2 }\).
  2. Find the value of a.
Edexcel M2 2014 June Q1
8 marks Moderate -0.3
  1. A van of mass 600 kg is moving up a straight road inclined at an angle \(\theta\) to the horizontal, where \(\sin \theta = \frac { 1 } { 16 }\). The resistance to motion of the van from non-gravitational forces has constant magnitude \(R\) newtons. When the van is moving at a constant speed of \(20 \mathrm {~m} \mathrm {~s} ^ { - 1 }\), the van's engine is working at a constant rate of 25 kW .
    1. Find the value of \(R\).
    The power developed by the van's engine is now increased to 30 kW . The resistance to motion from non-gravitational forces is unchanged. At the instant when the van is moving up the road at \(20 \mathrm {~m} \mathrm {~s} ^ { - 1 }\), the acceleration of the van is \(a \mathrm {~m} \mathrm {~s} ^ { - 2 }\).
  2. Find the value of \(a\).
Edexcel M2 2016 January Q1
8 marks Standard +0.3
  1. A car of mass 900 kg is travelling up a straight road inclined at an angle \(\theta\) to the horizontal, where \(\sin \theta = \frac { 1 } { 25 }\). The car is travelling at a constant speed of \(14 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and the resistance to motion from non-gravitational forces has a constant magnitude of 800 N . The car takes 10 seconds to travel from \(A\) to \(B\), where \(A\) and \(B\) are two points on the road.
    1. Find the work done by the engine of the car as the car travels from \(A\) to \(B\).
    When the car is at \(B\) and travelling at a speed of \(14 \mathrm {~ms} ^ { - 1 }\) the rate of working of the engine of the car is suddenly increased to \(P \mathrm {~kW}\), resulting in an initial acceleration of the car of \(0.7 \mathrm {~m} \mathrm {~s} ^ { - 2 }\). The resistance to motion from non-gravitational forces still has a constant magnitude of 800 N .
  2. Find the value of \(P\).
OCR M2 2006 June Q4
9 marks Moderate -0.3
4 A car of mass 900 kg is travelling at a constant speed of \(30 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) on a level road. The total resistance to motion is 450 N .
  1. Calculate the power output of the car's engine. A roof box of mass 50 kg is mounted on the roof of the car. The total resistance to motion of the vehicle increases to 500 N .
  2. The car's engine continues to work at the same rate. Calculate the maximum speed of the car on the level road. The power output of the car's engine increases to 15000 W . The resistance to motion of the car, with roof box, remains 500 N .
  3. Calculate the instantaneous acceleration of the car on the level road when its speed is \(25 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).
  4. The car climbs a hill which is at an angle of \(5 ^ { \circ }\) to the horizontal. Calculate the instantaneous retardation of the car when its speed is \(26 \mathrm {~ms} ^ { - 1 }\).
Edexcel M2 Q2
7 marks Standard +0.3
2. A car is travelling along a straight horizontal road against resistances to motion which are constant and total 2000 N . When the engine of the car is working at a rate of \(H\) kilowatts, the maximum speed of the car is \(30 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).
  1. Find the value of \(H\). The car driver wishes to overtake another vehicle so she increases the rate of working of the engine by \(20 \%\) and this results in an initial acceleration of \(0.32 \mathrm {~ms} ^ { - 2 }\). Assuming that the resistances to motion remain constant,
  2. find the mass of the car.
    (4 marks)
SPS SPS FM Mechanics 2026 January Q1
8 marks Standard +0.3
A van of mass 600 kg is moving up a straight road inclined at an angle \(\theta\) to the horizontal, where \(\sin \theta = \frac{1}{16}\). The resistance to motion of the van from non-gravitational forces has constant magnitude \(R\) newtons. When the van is moving at a constant speed of 20 m s\(^{-1}\), the van's engine is working at a constant rate of 25 kW.
  1. Find the value of \(R\). [4]
The power developed by the van's engine is now increased to 30 kW. The resistance to motion from non-gravitational forces is unchanged. At the instant when the van is moving up the road at 20 m s\(^{-1}\), the acceleration of the van is \(a\) m s\(^{-2}\).
  1. Find the value of \(a\). [4]