Chapter 11, Problem 37A

To determine

The increase in the kinetic energy of a sprinter if its velocity increases by three times.

Answer to Problem 37A

Kinetic energy increases by $9$ times.

Explanation of Solution

Given:

The final velocity is $3$ times the initial velocity, that is, $v_f=3v_i$ .

Formula used:

The kinetic energy of an object of mass $m$ travelling at a speed of $v$ is given by,

  $KE=\frac{1}{2}m{v}^2$

Calculation:

Let the initial velocity and the kinetic energy be,

  $K{E}_i=\frac{1}{2}m{v}_i^2$

Then, the final kinetic energy of the sprinter will be,

  $\begin{array}{c}K{E}_f=\frac{1}{2}m{v}_f^2\\ =\frac{1}{2}m{\left(3v_i\right)}^2\\ =9K{E}_i\end{array}$

Conclusion:

Thus, the sprinter’s kinetic energy will become $9$ times of the initial kinetic energy.