Example: Accelerating Car

Question:

A car weighs 3000.0 lbs and has an engine that develops 160 hp. How long will it take to accelerate to 65 mph assuming no friction?

Answer:

First we calculate the mass of the car, the power, and the speed in SI-units: (3000 lb)·(4.45 N/lb) = m·(9.8 m/s²) =>
m = 1360 kg
P = (160 hp)·(746 W/hp) = 1.19·10⁵ W
v = (65 mph) · (m/s/2.24 mph) = 29.0 m/s
Now we calculate the time from:
P = W/t => t = W/P
And finally we use the work energy theorem:
W = DK = m v²/ 2
Put it all together:
t = mv²/2P
= (1360 kg)·(29 m/s)² / (2·1.19·10⁵ W)
= 4.8 s

Well, we all know that this is too quick. In reality, a car with this horsepower is not a Ferrari might take 10 to 15 seconds to get to 65 mph. So what is wrong with our calculation? We did not take care of friction effects. But still, you can see that we can come up with the answers to pretty complicated questions from simple considerations of energy and power.