Question

A 1600-kg race car can go from 0 to 100km/h in 5.9s . What average power is required to do this?

Answer 1

You know that P=W/t, where P is power, W is work, and t is time. We have the time, but calculating work is a bit trickier. You probably know that W=Fd, but we don't have a distance (d), and we don't have a force (F), so this equation isn't very helpful.

However, in this question, all the work being done is going into accelerating the car - making it move. This means the total work being done by the motor is effectively translated into the final kinetic energy of the car. In other words, W = ½mv^2. Knowing this makes the problem simpler, because now we already have the variables we need to calculate kinetic energy - mass and speed. To calculate power:

\[P=\frac{\frac{1}{2}mv^2}{t}\]
Plug in your numbers (and make sure to convert from km/h to m/s) and you have your answer! Let me know if you have any questions!