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

Mar 16, 2018

The speed is $= - \frac{\sqrt{3}}{2} m {s}^{-} 1$

#### Explanation:

The speed is the derivative of the position

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

$v \left(t\right) = p ' \left(t\right) = - \sin \left(t - \frac{\pi}{3}\right)$

When $t = \frac{2}{3} \pi$

$v \left(\frac{2}{3} \pi\right) = - \sin \left(t - \frac{\pi}{3}\right) = - \sin \left(\frac{2}{3} \pi - \frac{\pi}{3}\right)$

$= - \sin \left(\frac{1}{3} \pi\right)$

$= - \frac{\sqrt{3}}{2} m {s}^{-} 1$