Question

The force applied against an object moving horizontally on a linear path is described by `F(x)= 4x^2+x`. By how much does the object's kinetic energy change as the object moves from `x in [ 0, 4]`?

Answer 1

By the work energy theorem, change in kinetic energy is the work done by the object.

It is given that, `F(x)=4x^2+x`

and `W = F.x` `color(white)(ppwwwppwwwpp)` `["let x be displacement"]`

`dW = F.dx`

Integrating this,

`intdW = intF.dx`

`intdW = int_0^4d(4x^2 + x).dx`

`W = [4x^3/3 + x^2/2]_0^4`

`W = 4(4)^3/3 + (4)^2/2`

`W = 4(4)^3/3 + (4)^2/2`

`W = 256/3 + 8 = 256/3 + 24/3 = 280/3 = 93.3 Ns`