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

Jun 8, 2017

The speed is $= 3$

#### Explanation:

The speed is the derivative of the position

$p \left(t\right) = \sin \left(3 t - \frac{1}{4} \pi\right) + 3$

$v \left(t\right) = 3 \cos \left(3 t - \frac{1}{4} \pi\right)$

When $t = \frac{3}{4} \pi$, we have

$v \left(\frac{3}{4} \pi\right) = 3 \cos \left(3 \cdot \frac{3}{4} \pi - \frac{1}{4} \pi\right)$

$= 3 \cos \left(\frac{9}{4} \pi - \frac{1}{4} \pi\right)$

$= 3 \cos \left(\frac{8}{4} \pi\right)$

$= 3 \cos \left(2 \pi\right)$

$= 3 \cdot 1$

$= 3$