# The position of an object moving along a line is given by p(t) = sin(t- pi /4) +1 . What is the speed of the object at t = pi/3 ?

May 2, 2017

The speed is $= 0.97 m {s}^{-} 1$

#### Explanation:

The speed is the derivative of the position.

$p \left(t\right) = \sin \left(t - \frac{\pi}{4}\right) + 1$

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

Therefore,

when $t = \frac{\pi}{3}$

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

$= \cos \left(\frac{\pi}{12}\right)$

$= 0.97 m {s}^{-} 1$