Question

A driver in a 2000 kg Porsche wishes to pass to pass a slow-moving school bus on a four-lane road. What is the average power in watts required to accelerate the sports car from 30 m/s to 60 m/s in 9 seconds

Answer 1

The average power is $3.0\cdot 10^6 W$

Explanation:

First of all, we calculate the work done to accelerate the car; according to the work-energy theorem, the work done is equal to the change in kinetic energy of the car:

$W=K_f -K_i= \frac{1}{2}mv^2-\frac{1}{2}mu^2$

where :

$K_f = \frac{1}{2}mv^2$ is the final kinetic energy of the car, with

m = 2000 kg is the mass of the car

v = 60 m/s is the final speed of the car

$K_i = \frac{1}{2}mu^2$ is the initial kinetic energy of the car, with

u = 30 m/s is initial speed of the car

Soolving:

$W=\frac{1}{2}(2000)(60)^2 - \frac{1}{2}(2000)(30)^2=2.7\cdot 10^6 J$

Now we can find the power required for the acceleration, which is given by

$P=\frac{W}{t}$

where

t = 9 s is the time elapsed

Solving:

$P=\frac{2.7\cdot 10^6}{9}=3.0\cdot 10^6 W$

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