Question

The power of engine of a car of mass 1200 kg is 25 kW. The minimum time required to reach a velocity of 90 km/h by the car after starting from rest is (please give explanation also)

Answer 1

v = 90 km/h = 90 x 5 / 18 = 25 m/s

power = change in kinetic energy / time taken


time taken = change in kinetic energy / power

=> time taken =
$( \frac{1}{2} \times m \times {v}^{2} ) \div power \\ = \frac{1}{2} \times 1200 \times \frac{ {25}^{2} }{25 \times 1000} \\ = 15 \: sec$

Answer 2

mass of the car = 1200 kg

Initial velocity (u) = 0

P = power of the engine of the car = 25 kW = 25000 Watt

t = time taken by the car to reach a velocity of 90 km/h starting from rest = ??

final velocity of the car(v) =90 km/h = 90(5/18) = 25 m/s

By work energy theorem,

Energy = 1/2(m(v-u))
= 1/2 (1200(25-0))
= 0.5×1200 ×625

We know,

Power × time = Energy

25000 × time = 0.5×1200×625

Time = 0.5×1200×625/25000

Time = 15 seconds