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

Nov 7, 2016

$s \left(5\right) \approx - 2.0$

#### Explanation:

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

The speed is the first derivative:

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

$s \left(5\right) \approx - 2.0$