# The position of an object moving along a line is given by p(t) = 4t - sin(( pi )/4t) . What is the speed of the object at t = 9 ?

May 15, 2017

The speed is $= 3.44 m {s}^{-} 1$

#### Explanation:

The velocity is the derivative of the position.

$p \left(t\right) = 4 t - \sin \left(\frac{\pi}{4} t\right)$

$v \left(t\right) = p ' \left(t\right) = 4 - \left(\frac{\pi}{4}\right) \cos \left(\frac{\pi}{4} t\right)$

Therefore,

$v \left(9\right) = 4 - \left(\frac{\pi}{4}\right) \cos \left(\frac{\pi}{4} \cdot 9\right) = 3.44 m {s}^{-} 1$