# The position of an object moving along a line is given by p(t) = sin(t- pi /2) +3 . What is the speed of the object at t = pi/6 ?

Dec 9, 2017

The speed is $= \frac{1}{2} m {s}^{-} 1$

#### Explanation:

The position of the object is

$p \left(t\right) = \sin \left(t - \frac{\pi}{2}\right) + 3 = - \cos \left(t\right) + 3$

The speed is the derivative of the position

$v \left(t\right) = p ' \left(t\right) = \sin t$

Therefore,

When $t = \frac{\pi}{6}$

The speed is

$v \left(\frac{\pi}{6}\right) = \sin \left(\frac{\pi}{6}\right) = \frac{1}{2}$