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

Dec 11, 2017

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

#### Explanation:

The speed is the derivative of the position.

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

$v \left(t\right) = p ' \left(t\right) = 1 + \frac{\pi}{2} \sin \left(\frac{\pi}{2} t\right)$

Therefore, when $t = 2$

$v \left(2\right) = 1 + \frac{\pi}{2} \sin \left(\frac{\pi}{2} \cdot 2\right)$

$= 1 + \frac{\pi}{2} \sin \left(\pi\right)$

$= 1 - 0$

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