# The position of an object moving along a line is given by p(t) = 3t - 2sin(( pi )/8t) + 2 . What is the speed of the object at t = 12 ?

Jun 9, 2016

I found: $3 \frac{m}{s}$
We can find the instantaneous speed by deriving with respect to $t$ and evaluate the derivative at $t = 12$:
$s \left(t\right) = p ' \left(t\right) = \frac{\mathrm{dp} \left(t\right)}{\mathrm{dt}} = 3 - 2 \frac{\pi}{8} \cos \left(\frac{\pi}{8} t\right) + 0 =$
$= 3 - \frac{\pi}{4} \cos \left(\frac{\pi}{8} t\right)$
at $t = 12$
$s \left(12\right) = 3 - \frac{\pi}{4} \cos \left(\frac{\pi}{8} \cdot 12\right) = 3 + 0 = 3 \frac{m}{s}$