# The position of an object moving along a line is given by p(t) = cos(t- pi /3) +2 . What is the speed of the object at t = (2pi) /4 ?

v(t) =(dp)/(dt) =d/(dt) cos(t-pi/3)+2 =-sin(t-pi/3)
At $t = \frac{2 \pi}{4}$,
$v \left(t\right) = - \sin \left(\frac{2 \pi}{4} - \frac{\pi}{3}\right) = - \sin \left(\frac{\pi}{6}\right) = - 0.5$