The engine of a 1540-kg automobile has a power rating of 75 kW. Determine the time required to accelerate this car from rest to a speed of 100 km/h at full power on a level road. Is your answer realistic?

7.92 s

Explanation:

Power: This can be defined as the rate at which energy is used. The S. I unit of

Watt (W).

Mathematically power can be represented as,

P = E/t

Pt = E ... Equation 1

Where P = power of the engine, t = time, E = Energy.

But,

E = 1/2m (Δv) ² ... Equation 2

Where m = mass of the automobile, Δv = change in velocity of the car = final velocity - initial velocity.

Substitute the value of E in equation 2 into equation 1

Pt = 1/2m (Δv) ² ... Equation 3

making t the subject of the equation,

t = 1/2m (Δv) ²/P ... Equation 4

Given: m = 1540 kg, P = 75 kW = 75000 W, Δv = 100-0 = 100 km/h (initial velocity of the car = 0 km/h)

100 (1000/3600) m/s = 27.78 m/s

Substitute into equation 4

t = 1/2 (1540) (27.78) ²/75000

t = 594230.87/75000

t = 7.92 second.

Thus The time required to accelerate the car = 7.92 seconds.

It is not realistic period the time period is too short.