Question

A police car of mass 2.4x103kg is travelling on the highway when the officers receive an emergency call. They increase the speed of the car to 33 m/s.  The increase in speed results in 3.1 x 10 5 J of work done on the car. Determine the initial speed of the police car in kilometers per hour?

Answer 1

Given:

$m=\rm2.4*10^3\: kg$

$v_f=\rm 33\: m/s$

$W=3.1*10^5\:\rm J$

The energy-work theorem says

$$W=\Delta E=\frac{mv_f^2}{2}-\frac{mv_i^2}{2}$$

Hence, the initial speed

$$v_i=\sqrt{v_f^2-2W/m}$$

$$v_i=\sqrt{33^2-2*3.1*10^5/2.4*10^3}=29\:\rm m/s$$