CAIE M1 2022 June — Question 6

Exam BoardCAIE
ModuleM1 (Mechanics 1)
Year2022
SessionJune
TopicWork, energy and Power 1

6 A car of mass 900 kg is moving up a hill inclined at \(\sin ^ { - 1 } 0.12\) to the horizontal. The initial speed of the car is \(11 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). After 12 s, the car has travelled 150 m up the hill and has speed \(16 \mathrm {~ms} ^ { - 1 }\). The engine of the car is working at a constant rate of 24 kW .
  1. Find the work done against the resistive forces during the 12 s .
    The car then travels along a straight horizontal road. There is a resistance to the motion of the car of \(( 1520 + 4 v ) \mathrm { N }\) when the speed of the car is \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\). The car travels at a constant speed with the engine working at a constant rate of 32 kW .
  2. Find this speed.