# The force applied against an object moving horizontally on a linear path is described by #F(x)=x^2-3x + 3 #. By how much does the object's kinetic energy change as the object moves from # x in [ 0 , 1 ]#?

##### 1 Answer

Newton's second law of motion:

Definitions of acceleration and velocity:

Kinetic energy:

Answer is:

#### Explanation:

Newton's second law of motion:

Substituting

But

Substituting into the equation we have, we have a differential equation:

The two speeds are unknown but the positions

But

**Note** : the units are