Question

A car with a mass of 1.50 X 10^3 kg starts from rest and accelerates to a speed of 18.0 m/s in 12.0 s. Assume that the force of resistance remains constant at 400.0 N during this time. what is the average power developed by the car's engine?

Answer 1

The average power is 20.3 kW

Explanation:

First of all, we calculate the work done on the car: the work-energy theorem states that the work done on the car is equal to the change in kinetic energy of the car, so we have

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

where

W is the work done

$K_i, K_f$ are the initial and final kinetic energy of the car

$m=1.50\cdot 10^3 kg = 1500 kg$ is the mass of the car

u = 0 is the initial velocity

v = 18.0 m/s is the final velocity

Substituting,

$W=\frac{1}{2}(1500)(18)^2=2.43\cdot 10^5 J$

Now we can find the average power developed by the car's engine, which is given by

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

where

$W=2.43\cdot 10^5 J$ is the work done

t = 12.0 s is the time taken

Substituting,

$P=\frac{2.43\cdot 10^5 J}{12.0}=20,250 W = 20.3 kW$

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