# The position of an object moving along a line is given by p(t) = 2t^3 - 5t^2 +2. What is the speed of the object at t = 2 ?

Aug 3, 2017

I got $4 \frac{m}{s}$

#### Explanation:

We can derive our position function to find the average velocity and then evaluate it a our instant to get the instantaneous one.
We get:

$v \left(t\right) = \frac{\mathrm{dp} \left(t\right)}{\mathrm{dt}} = 6 {t}^{2} - 10 t$

at $t = 2$

$v \left(2\right) = 6 \cdot 4 - 10 \cdot 2 = 24 - 20 = 4 \frac{m}{s}$