# The position of an object moving along a line is given by p(t) = 7t - cos(( pi )/3t) + 2 . What is the speed of the object at t = 13 ?

Jan 20, 2018

The speed is $= 7.91 m {s}^{-} 1$

#### Explanation:

The speed is the derivative of the position

$p \left(t\right) = 7 t - \cos \left(\left(\frac{\pi}{3}\right) t\right) + 2$

$v \left(t\right) = 7 + \left(\frac{\pi}{3}\right) \sin \left(\frac{\pi}{3}\right) \cdot t$

When $t = 13$, the speed is

$v \left(13\right) = 7 + \left(\frac{\pi}{3}\right) \sin \left(\left(\frac{\pi}{3}\right) \cdot 13\right)$

$= 7.91 m {s}^{-} 1$