The position of an object moving along a line is given by p(t) = 3t - cos(( pi )/8t) + 2 . What is the speed of the object at t = 7 ?

Feb 28, 2017

$\text{The speed of object at t=7 is v(7)=3.78}$

Explanation:

$\frac{d p \left(t\right)}{d t} = v \left(t\right)$

$\frac{d p \left(t\right)}{d t} = 3 + \frac{\pi}{8} \cdot \sin \left(\frac{\pi}{8} t\right) + 0$

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

$v \left(7\right) = 3 + \frac{\pi}{8} + \sin \left(\frac{\pi}{8} \cdot 7\right)$

$\sin \left(\frac{7 \pi}{8}\right) = 0.38268343$

$v \left(7\right) = 3 + \frac{\pi}{8} + 0.38268343$

$v \left(7\right) = \frac{\pi}{8} + 3.38268343$

$\frac{\pi}{8} = 0.39269908$

$v \left(7\right) = 0.39269908 + 3.38268343 = 3.7753825$

$v \left(7\right) = 3.78$