## Fundamentals of Physics Extended (10th Edition)

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 $24(3) - 6(2)^2 = 72 - 24 = 48m/s$