Question

The velocity of an object with a mass of `2 kg` is given by `v(t)= t^3 + 3 t^2`. What is the impulse applied to the object at `t= 4`?

Answer 1

`I (4) =2 (4*4^2 +3*4^2) = 7*4^2 = 112 N s`
Careful however Impulse is not `mv(t)` evaluate at `t = 4 s`
it is Force applied for a finite amount of time `F*Deltat`
in the limit `I = int_(t_1)^(t_(2))Fdt`

Explanation:

This is a straight implementation of the impulse equation i.e.
`F = m(dv)/dt` Newton law ==> (1)
`I = F dt = m(dv)` Impulse equation ==> (2)
While the question is not clear I will make the assumption the Force was applied for 4 seconds causing the change in speed from
`v(0) = 0 -> v(4)` and `I (4) =2 (4*4^2 +3*4^2) = 7*4^2 = 112 N s`