# 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 = 3 ?

Jun 19, 2017

The speed is $= 4.56 m {s}^{-} 1$

#### Explanation:

The speed is the derivative of the position.

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

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

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

When $t = 4$, we have

$v \left(4\right) = 4 - \frac{\pi}{4} \cos \left(\frac{3}{4} \pi\right)$

$= 4 + 0.56$

$= 4.56$