Chapter 11.1, Problem 2PP

To determine

Initial and final kinetic energy of car and work done in increasing the speed of the car.

Answer to Problem 2PP

Initial kinetic energy of car is 211750 J, final kinetic energy of car is 847000 J and work done in increasing the speed of car is 635250 J

Explanation of Solution

Given:

Mass of bicycle, $m=875\text{ kg}$

Initial speed of bicycle, $u=22\text{ m/s}$

Final velocity of bicycle, $v=44\text{ m/s}$

Formula used:

  $KE=\frac{1}{2}m{v}^2$

Here, KE is kinetic energy, m is mass and vis velocity.

Calculation:

Initial kinetic energy of car is:

  $\begin{array}{l}K{E}_i=\frac{1}{2}m{u}^2\\ =\frac{1}{2}\times 875\times {22}^2\\ =211750\text{ J}\end{array}$

Final kinetic energy of car is:

  $\begin{array}{l}K{E}_f=\frac{1}{2}m{v}^2\\ =\frac{1}{2}\times 875\times {44}^2\\ =847000\text{ J}\end{array}$

According to work energy theorem work done is equal to change in kinetic energy.

Therefore,

  $\begin{array}{l}W=K{E}_f-K{E}_i\\ =847000-211750\\ =635250\text{ J}\end{array}$

So the work done in increasing the speed of car is 635250 J.