A car accelerates from rest to 100 ms−1 in 10 seconds. If mass of the car

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A car accelerates from rest to 100

m s^{- 1}

in 10 seconds. If mass of the car is 50 kg then power developed by the engine is:

Options:

A . 20 kW

B . 25 kW

C . 30 kW

D . 35 kW

Answer: Option B
:
B
Given, mass of the body

m = 50 k g

, initial velocity

u = 0 m s^{- 1}

, velocity

v = 100 m s^{- 1}

and time

t = 10 s

.
The change in kinetic energy of the car would be equal to the work done by the engine.
Since, power is work done per unit time, so change in kinetic energy of the car and the time taken for that change would give us the power developed by the engine.
i.e.Work done

= \frac{1}{2} \times m \times v^{2} - \frac{1}{2} \times m \times u^{2} = \frac{1}{2} \times 50 \times 100^{2} - \frac{1}{2} \times 50 \times 0^{2} = 250000 J

.
Power

= \frac{W o r k}{T i m e} = \frac{250000}{10} = 25000 W = 25 k W

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