The position of an object moving along a line is given by p(t) = 2t - cos(( pi )/6t) . What is the speed of the object at t = 3 ?

Apr 5, 2018

The speed is $= 2.52 m {s}^{-} 1$

Explanation:

The speed is the derivative of the position

$p \left(t\right) = 2 t - \cos \left(\frac{\pi}{6} t\right)$

$v \left(t\right) = p ' \left(t\right) = 2 + \frac{\pi}{6} \sin \left(\frac{\pi}{6} t\right)$

And when $t = 3$

$v \left(3\right) = 2 + \frac{\pi}{6} \sin \left(\frac{\pi}{6} \cdot 3\right)$

$= 2 + \frac{\pi}{6} \sin \left(\frac{\pi}{2}\right)$

$= 2 + \frac{\pi}{6}$

$= 2.52 m {s}^{-} 1$