# The position of an object moving along a line is given by p(t) = t - tsin(( pi )/3t) . What is the speed of the object at t = 1 ?

Apr 28, 2017

$p ' \left(1\right) \approx - 0.389$ distance units/time units

#### Explanation:

The speed of the object at any given time, ${t}_{1}$, is the first derivative, $p ' \left(t\right)$, evaluated that time.

Compute the first derivative:

$p ' \left(t\right) = 1 - \sin \left(\frac{\pi}{3} t\right) - \frac{\pi}{3} t \cos \left(\frac{\pi}{3} t\right)$ distance units/time units

Evaluate at t = 1:

$p ' \left(1\right) \approx - 0.389$ distance units/time units