CAIE M1 2019 June — Question 6

Exam BoardCAIE
ModuleM1 (Mechanics 1)
Year2019
SessionJune
TopicWork, energy and Power 1

6 A car has mass 1000 kg . When the car is travelling at a steady speed of \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\), where \(v > 2\), the resistance to motion of the car is \(( A v + B ) \mathrm { N }\), where \(A\) and \(B\) are constants. The car can travel along a horizontal road at a steady speed of \(18 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) when its engine is working at 36 kW . The car can travel up a hill inclined at an angle of \(\theta\) to the horizontal, where \(\sin \theta = 0.05\), at a steady speed of \(12 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) when its engine is working at 21 kW . Find \(A\) and \(B\).