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

the minimum amperage that the current in this wire would have to have so that its weight is completely supported by the magnetic force due to earth's field, assuming that no other forces except gravity act on it