Question

An object moves along the x-axis so that its velocity at any time `t >=0` is given by `v(t) = 4t^3 - 4t`. What is the displacement of the particle from `t=0` to `t=2`?

Answer 1

`Delta x=8`

Explanation:

`Delta x=int _0^2 v(t) d t`

`Delta x=int_0^2 (4t^3-4t)d t`

`Delta x=|cancel(4)*x^4/cancel(4)-cancel(4)*x^2/cancel(2)|_0^2`

`Delta x=|x^4-2x^2|_0^2`

`Delta x=(2^4-2*2^2)-(0)`

`Delta x=16-8=8`