# The position of an object moving along a line is given by p(t) = sin(2t- pi /8) +2 . What is the speed of the object at t = (2pi) /3 ?

Nov 22, 2016

I found: $- 1.6 \frac{m}{s}$

#### Explanation:

I would derive the time function to get the velocity as:
$v \left(t\right) = \frac{\mathrm{dp}}{\mathrm{dt}} = 2 \cos \left(2 t - \frac{\pi}{8}\right)$
at $t = \frac{2 \pi}{3}$ we get:
$v \left(\frac{2 \pi}{3}\right) = 2 \cos \left(2 \frac{2 \pi}{3} - \frac{\pi}{8}\right) = - 1.6 \frac{m}{s}$