# The position of an object moving along a line is given by p(t) = 2t^3 - 2t^2 +2. What is the speed of the object at t = 6 ?

Mar 9, 2017

$\text{the answer : } v \left(6\right) = 192$

#### Explanation:

$\text{notice : } \frac{d}{d t} = v \left(t\right)$

$\text{where v is speed}$

$\text{we should find "(d)/(d t) p(t)" for the time t=6}$

$\frac{d}{d t} p \left(t\right) = v \left(t\right) = 3 \cdot 2 {t}^{2} - 2 \cdot 2 \cdot {t}^{1} + 0$

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

$v \left(6\right) = 6 \cdot {6}^{2} - 4 \cdot 6$

$v \left(6\right) = 216 - 24$

$v \left(6\right) = 192$