Question

A car of weight 20000 N climbs up a hill at a steady speed of 8 m/s, gaining a height of 120 m is 100 s. Calculate :
(a) work done by the car.
(b) power of engine of car.

Answer 1

(a) Weight of the car, (W) = 20000 N
Height, (h) = 120 m
Time taken, (t) = 100 s
We can calculate the work done against gravity as,
Work done by the car = Weight of body × Vertical distance
= 20000 × 120 J
= 2400000
$=\boxed{2.4\times {10}^6\mathrm{J}}$
(b) Now, we can calculate the power of the body as,
$$\begin{gathered} \mathrm{Power}=\frac{\mathrm{Work}\mathrm{done}}{\mathrm{Time}} \\ \mathrm{So}, \\ \mathrm{Power}=\frac{2400000}{100}\mathrm{W} \\ =\boxed{24\mathrm{kW}} \end{gathered}$$
So, the power of car is 24 kW.