Answer
velocity = 48m/s
Work Step by Step
The position is given by $ x = 12t^2 - 2t^3 $
Since the velocity equation is the derivative of the position equation we need to find
$\frac{d}{dt} (12t^2 - 2t^3) $
Since $\frac{d}{dt} t^n = n*t^(n-1)$ then
$\frac{d}{dt} (12t^2 - 2t^3) = 12(2)t - 2(3)t^2 = 24t - 6t^2 $
To find the velocity at t =3, we need to plug this into the velocity equation
This gives us $ 24(3) - 6(2)^2 = 72 - 24 = 48m/s$
