# How much work would it take to horizontally accelerate an object with a mass of #8 # #kg# to #5# # ms^-1# on a surface with a kinetic friction coefficient of #5 #?

##### 1 Answer

See the explanation below for how this expression was derived.

#### Explanation:

(just a quick side note that a friction coefficient of

There are two components of the force required. The first overcomes the inertia of the object in accordance with Newton's Second Law :

The second overcomes the frictional force:

So the total force is:

The work done is the force exerted times the distance travelled:

Of the things in this expression we are given

We're told a final velocity of

If we assume a value for the acceleration,

Remembering

We can substitute these values into our expression for the work:

Here's an extension question for you: if we assumed a different number for the acceleration, would the work done be the same? Why or why not? Answer (write it down so you can't change your mind until you find out!) and then try it with