# An object with a mass of #8 kg# is moving at #7 m/s# over a surface with a kinetic friction coefficient of #6 #. How much power will it take to accelerate the object at #8 m/s^2?

##### 1 Answer

#### Explanation:

As the object moves on a horizontal surface with friction, it looses kinetic energy. Friction converts its kinetic energy to thermal energy and dissipates it out. So to keep the object moving at a constant speed, external energy must be imparted at the same rate as its kinetic energy is dissipated out by friction.

First let us arrive at a relation connecting the power

**Power**: Power is defined as the rate at which energy is delivered-to or drawn-from a system. Here we are concerned with the mechanical energy, which is the sum of potential and kinetic energies :

Since the object is moving on a horizontal surface there is no change in potential energy (

By the **Work-Energy Theorem**, total work done is equal to the change in kinetic energy:

The force doing the work here is the frictional force:

Work done

Therefore,

This expression gives the power required to keep an object of mass

Given:

So, to accelerate the body from a speed of