# An object of mass, $m$ is moving with a constant velocity, $v$. How much work should be done on the object in order to bring the object to rest?

#### Complete Python Prime Pack

9 Courses     2 eBooks

#### Artificial Intelligence & Machine Learning Prime Pack

6 Courses     1 eBooks

#### Java Prime Pack

9 Courses     2 eBooks

Given:

An object of mass, $m$ is moving with a constant velocity, $v$.

To do:

We have to calculate the work that should be done on the object in order to bring the object to rest.

Solution:

As given, the mass of the object$=m$

The velocity of the moving object$=v$

Therefore, the kinetic energy of the moving object $K_1=\frac{1}{2}mv^2$

When the object will come to rest, its velocity will become zero.

$v=0$

Therefore, the kinetic energy of the object at rest, $K_2=0$

Let $W$ be the work that should be done on the given moving object to bring it to rest and this work done will be equal to the change in its kinetic energy.

Therefore, work done to bring the object at rest$=$Change in energy

Or work done$=K_2-K_1$

$=0-\frac{1}{2}mv^2$

$=-\frac{1}{2}mv^2$

Thus, work done to bring the object to rest is $-\frac{1}{2}mv^2$. $( -ve)$ sign indicates work done opposite to the direction.

Updated on 10-Oct-2022 13:22:57