# The position of an object moving along a line is given by p(t) = 4t - tsin(( pi )/8t) . What is the speed of the object at t = 7 ?

Oct 12, 2017

I tried this (but check my maths):

#### Explanation:

To find the velocity we can derive the function of position (in meter I think) with respect to $t$:

$v \left(t\right) = \frac{\mathrm{dp} \left(t\right)}{\mathrm{dt}} = 4 - \left[\sin \left(\frac{\pi}{8} t\right) + \frac{\pi}{8} t \cos \left(\frac{\pi}{8} t\right)\right]$

Let us now evaluate this at $t = 7$ (seconds, I think):

$v \left(7\right) = 4 - \left[\sin \left(\frac{\pi}{8} \cdot 7\right) + \frac{\pi}{8} \cdot 7 \cos \left(\frac{\pi}{8} \cdot 7\right)\right] = 6.1 \frac{m}{s}$