A motorist driving a 1000-kg car wishes to increase her speed from 20 m/s to 30 m/s in 5 s. Determine the horsepower required to accomplish this increase. Neglect friction.

13.41 horsepower

Explanation:

Power: This can be defined as the rate at which energy is used up by a body. The S. I unit of power is Watt (W).

The expression for power is given as,

P = Ek/t ... Equation 1

Where P = power, Ek = Kinetic Energy of the car, t = time.

Recall that,

Ek = 1/2mΔv² ... Equation 2

Where m = mass of the car, Δv = change in velocity of the car.

Substitute equation 2 into equation 1

P = 1/2 (mΔv²) / t ... Equation 3

Given:m = 1000 kg, Δv = 30-20 = 10 m/s, t = 5 s

Substitute into equation 3

P = 1/2 (1000*10²) / 5

P = 10000 W.

If,

745.7 W = 1 hp,

Then,

10000 W = (10000/745.7) hp

= 13.41 hp.

P = 13.41 horsepower