Question

A body moves s metres in a time t seconds so that s = t3 – 3t2 + 8. Find:

i) the velocity, v, after t seconds

Answer 1

Answer is 3t²-6t

Step-by-step Step-by-step explanation:-

`s(t) = {t}^(3) - 3 {t}^(2) + 8`

Now we need to find velocity. The velocity is the first derivative of position, so let's find the derivative of s(t) :-

`s'(t) = v(t) = 3 {t}^(3 - 1) - 3 * 2 {t}^(2 - 1)`

So,

`v(t) = 3 {t}^(2) - 6t`

Therefore, v(t) = 3t²-6t