# The position of an object moving along a line is given by p(t) = 2t^3 - 2t^2 +1. What is the speed of the object at t = 4 ?

May 3, 2016

$v \left(4\right) = 80$

#### Explanation:

$v \left(t\right) = \frac{d}{d t} p \left(t\right)$

$v \left(t\right) = \frac{d}{d t} \left(2 {t}^{3} - 2 {t}^{2} + 1\right)$

$v \left(t\right) = 6 {t}^{2} - 4 t + 0$

"if" " t=4 " ->" "v(4)=6*4²-4*4=96-16=80

$v \left(4\right) = 80$