Question

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

Answer 1

It increases by `4"J"`

Explanation:

Work done = force x distance moved in direction of force.

Because force varies with displacement we can say:

`W=int_1^2F.dx`

`:.W=int_1^2(x+3).dx`

`W=[x^2/2+3x]_1^2`

`W=[4/2+6]-[1+3]`

`W=8-4=4"J"`

This work will appear as kinetic energy.