Question

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

Answer 1

The change in kinetic energy will be `3` joules.

Explanation:

Recall that `"Work" = F * d = Delta KE`

Therefore, if we find `F * d` one `[0, 3]`, we'll have our change in kinetic energy. Therefore, we will have to integrate the force function on `[0, 3]`.

`I = int_0^3 cos(pix) + 1`

`I = [1/pi sin(pix) + x]_0^3`

`I = 1/pisin(3pi) + 3 - 1/pisin(0) - 0`

`I = 3`

Therefore the change in kinetic energy will be `3` Joules.

Hopefully this helps!