# The position of an object moving along a line is given by p(t) = 2t - sin(( pi )/6t) . What is the speed of the object at t = 16 ?

Nov 9, 2016

The speed is $= 2 + \frac{\pi}{12}$

#### Explanation:

If the position is $p \left(t\right) = 2 t - \sin \left(\frac{\pi}{6} t\right)$
Then the velocity is given by the derivative of $p \left(t\right)$
$\therefore v \left(t\right) = 2 - \frac{\pi}{6} \cos \left(\frac{\pi}{6} t\right)$
When $t = 16$
$v \left(16\right) = 2 - \frac{\pi}{6} \cos \left(\frac{\pi}{6} \cdot 16\right)$
$= 2 - \frac{\pi}{6} \cos \left(\frac{8}{3} \pi\right) = 2 - \frac{\pi}{6} \cdot \left(- \frac{1}{2}\right)$
$= 2 + \frac{\pi}{12}$