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.

the answer is a)

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