What is the horsepower needed to change the speed of a 1600-kg sport utility vehicle from 15.0 m/s to 40.0 m/s in 4.00 seconds?
A) 369 hp
B) 36.9 hp
C) 18.8 hp
D) 188 hp
E) 275 hp

Question

Quizplus · Accepted Answer

The formula to calculate horsepower is:

Horsepower = (Force x Distance) / Time

We need to first calculate the force required to change the speed of the SUV:

Force = (mass x change in velocity) / time

∆v = 40 - 15 = 25 m/s

Force = (1600 kg x 25 m/s) / 4 s

Force = 10,000 N

Now we can calculate the horsepower:

Horsepower = (Force x Distance) / Time

We don't have the distance, but we can assume it's the average distance traveled during acceleration, which is:

Distance = (initial velocity + final velocity) / 2 x time

Distance = ((15 m/s + 40 m/s) / 2) x 4 s

Distance = 100 m

Horsepower = (10,000 N x 100 m) / 4 s

Horsepower = 250,000 J/s / 746 W/hp

Horsepower = 334.7 hp

Therefore, the answer is closest to choice A (369 hp).

What Is the Horsepower Needed to Change the Speed of a 1600-Kg