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.

Question

Quizplus · Accepted Answer

The change in kinetic energy of the car can be calculated as

ΔK = (1/2)mv²_f - (1/2)mv²_i

where m is the mass of the car, v_i is the initial velocity, and v_f is the final velocity. Substituting the given values, we get

ΔK = (1/2)(1000 kg)(30 m/s)² - (1/2)(1000 kg)(20 m/s)² = 1.5 million J

The average power required to accomplish this change in 5 seconds is

P = ΔK/t = (1.5 million J)/(5 s) = 300,000 W

Converting to horsepower, we get

P = 300,000 W × (1 hp/746 W) = 402 hp

Therefore, the horsepower required to accomplish this increase is more than 70 hp, but the closest option is C, 70 hp.

A Motorist Driving a 1000-Kg Car Wishes to Increase Her