Constant power on horizontal road

A question is this type if and only if a vehicle moves on a horizontal road with constant engine power, and you must find acceleration, steady speed, or use P=Fv with constant resistance.

4 questions · Standard +0.1

6.02l Power and velocity: P = Fv
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CAIE M1 2004 June Q6
8 marks Moderate -0.3
6 A car of mass 1200 kg travels along a horizontal straight road. The power of the car's engine is 20 kW . The resistance to the car's motion is 400 N .
  1. Find the speed of the car at an instant when its acceleration is \(0.5 \mathrm {~m} \mathrm {~s} ^ { - 2 }\).
  2. Show that the maximum possible speed of the car is \(50 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). The work done by the car's engine as the car travels from a point \(A\) to a point \(B\) is 1500 kJ .
  3. Given that the car is travelling at its maximum possible speed between \(A\) and \(B\), find the time taken to travel from \(A\) to \(B\).
CAIE M1 2013 June Q4
6 marks Standard +0.3
4 A train of mass 400000 kg is moving on a straight horizontal track. The power of the engine is constant and equal to 1500 kW and the resistance to the train's motion is 30000 N . Find
  1. the acceleration of the train when its speed is \(37.5 \mathrm {~m} \mathrm {~s} ^ { - 1 }\),
  2. the steady speed at which the train can move.
CAIE M1 2008 November Q3
6 marks Standard +0.3
3 A car of mass 1200 kg is travelling on a horizontal straight road and passes through a point \(A\) with speed \(25 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). The power of the car's engine is 18 kW and the resistance to the car's motion is 900 N .
  1. Find the deceleration of the car at \(A\).
  2. Show that the speed of the car does not fall below \(20 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) while the car continues to move with the engine exerting a constant power of 18 kW .
CAIE M1 2009 November Q3
6 marks Standard +0.3
3 A car of mass 1250 kg travels along a horizontal straight road with increasing speed. The power provided by the car's engine is constant and equal to 24 kW . The resistance to the car's motion is constant and equal to 600 N .
  1. Show that the speed of the car cannot exceed \(40 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).
  2. Find the acceleration of the car at an instant when its speed is \(15 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).