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

Oct 25, 2016

velocity $v = p ' = \cos \left(t - \frac{\pi}{4}\right)$
$v \left(\frac{\pi}{4}\right) = \cos 0 = 1$
Speed is $s = \left\mid v \right\mid = 1$