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 = 2 ?

May 19, 2017

$3.7 \frac{m}{s}$

Explanation:

The equation for instantaneous velocity ${v}_{x}$ is the derivative of the position equation ($\frac{d}{\mathrm{dx}} \sin \left(a x\right) = a \cos \left(a x\right)$)

${v}_{x} \left(t\right) = 4 \frac{m}{s} - \frac{\pi}{8} \cos \left(\frac{\pi}{8} \frac{m}{s} t\right)$

At time $t = 2.0 s$, the velocity is

${v}_{x} \left(2.0\right) = 4 \frac{m}{s} - \frac{\pi}{8} \cos \left(\frac{\pi}{8} \frac{m}{s} \left(2.0 s\right)\right) = 3.7 \frac{m}{s}$