Question:

A car of weight W is on an inclined road that rises by 100m over a distance of 1km and applies a constant frictional force W/20 on the car. While moving uphill on the road at a speed of 10ms⁻¹, the car needs power P. If it needs power P₂ while moving downhill at speed v, then the value of v is:

10ms⁻¹

20ms⁻¹

5ms⁻¹

15ms⁻¹

Let us apply the work-energy theorem in this question. In the first case,

100W + W/20 × 1000 = Pt = P × (1000/10)
P = 1.5W

In the downhill case, gravity will support the motion, hence,

100W - W/20 = P₂t₂ = 1.5Wt₂
t₂ = 1000/15 s
Hence, v = 1000/(1000/15) = 15m/s