# How do you find the average velocity of the position function s(t)=3t^2-6t on the interval from t=2 to t=5?

Given, $s = 3 {t}^{2} - 6 t$
So,displacement in between $2 s$ and $5 s$ is $s = 3 {\left[{t}^{2}\right]}_{2}^{5} - 6 {\left[t\right]}_{2}^{5} = 3 \left(25 - 4\right) - 6 \left(5 - 2\right) = 45 m$
So,average velocity =$\frac{45}{5 - 2} = 15 m {s}^{-} 1$