# The position of an object moving along a line is given by p(t) = 2t - t^2cos(( pi )/3t) . What is the speed of the object at t = 5 ?

$p \left(t\right) = 2 t - {t}^{2} \cos \left(\frac{\pi}{3} t\right)$
$v \left(t\right) = \dot{p} \left(t\right) = 2 + 2 \frac{\pi}{3} t \sin \left(\frac{\pi}{3} t\right)$
$v \left(5\right) = 2 + \frac{2 \pi}{3} \cdot 5 \cdot \sin \left(\frac{5 \pi}{3}\right) \approx 2 + \frac{2 \pi}{3} \cdot 5 \cdot \left(- 0.87\right) = - 7.11$