# The force applied against an object moving horizontally on a linear path is described by #F(x)= 4x+3 N #. By how much does the object's kinetic energy change as the object moves from # x in [ 1 , 3 ]#?

##### 1 Answer

Given force applied against an object moving horizontally on a linear path

where it is assumed

Since the object moves horizontally on a linear path, we can assume that potential energy of the object does not change. As such only change is in its kinetic energy due to work done against the force.

We know that work done

Since both force and direction of motion are co-linear angle between the two is

As the force moves through distance

Inserting value of force from (1) we have