# The position of an object moving along a line is given by p(t) = 3t - 2cos(( pi )/8t) + 2 . What is the speed of the object at t = 3 ?

Apr 14, 2016

3.016

#### Explanation:

The position is given as

$p \left(t\right) = 3 t - 2 \cos \left(\frac{\pi}{8} t\right) + 2$

Hence, the speed is given as

$v \left(t\right) = \frac{\mathrm{dp}}{\mathrm{dt}} = 3 + 2 \frac{\pi}{8} \sin \left(\frac{\pi}{8} t\right)$

Hence the speed at $t = 3$ is:

$v \left(3\right) = 3 + 2 \frac{\pi}{8} \cdot \sin \left(\frac{3 \pi}{8}\right) \approx 3.016$