Chapter 10.1, Problem 15SSC

To determine

Whether the speed of an object will also be doubled or not if the work done on it doubles its kinetic energy.

Answer to Problem 15SSC

Speed will not be doubled, but it will become $\sqrt{2}$ times of the initial speed.

Explanation of Solution

Introduction:

The kinetic energy of an object is given by

  $KE=\frac{1}{2}m{v}^2$

Where m is the mass of the object and v is the velocity of the object.

Let the initial Kinetic energy of an object be,

  $K{E}_i=\frac{1}{2}m{v}_i^2$

Then, if the work done in it doubles its kinetic energy, then its new velocity will be,

  $\begin{array}{c}K{E}_n=\frac{1}{2}m{v}_n^2\\ 2K{E}_i=\frac{1}{2}m{v}_n^2\\ 2\left(\frac{1}{2}m{v}_i^2\right)=\frac{1}{2}m{v}_n^2\\ v_n=v_i\sqrt{2}\end{array}$

Conclusion:

Thus, if the work done doubles the kinetic energy of an object, then it speed will become $\sqrt{2}$ times of the initial speed.