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

Jul 20, 2018

The speed of the object at $t = 8$ is approximately $s = 120.8 \frac{m}{s}$

#### Explanation:

I will be rounding to the nearest decimal place for convenience

Speed is equal to distance multiplied by time, $s = \mathrm{dt}$

First, you want to find the position of the object at $t = 8$ by plugging in $8$ for $t$ in the given equation and solve

$p \left(8\right) = 2 \left(8\right) - \sin \left(\frac{8 \pi}{3}\right)$
$p \left(8\right) = 16 - \frac{\sqrt{3}}{2}$

$p \left(8\right) = 15.1$

Assuming that $t$ is measured in seconds and distance ($d$)is measured in meters, plug into the speed formula

$s = \mathrm{dt}$

$s = 15.1 m \cdot 8 s$

$s = 120.8 \frac{m}{s}$