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

Jul 6, 2016

$v \left(t\right) = 3 - \setminus \frac{\sqrt{3}}{2} - \frac{\pi}{3}$

#### Explanation:

Given, the position function of an object is
$p \left(t\right) = 3 t - t \sin \left(\frac{\pi}{6} t\right)$

The velocity/speed of an object at a point can be found by taking the time derivative of the position function when it is with respect to time. (They can't come with respect to position thankfully).

So, the derivative of the position function now gives (because I'm sure you learnt differentiation)
$v \left(t\right) = 3 - \sin \left(\setminus \frac{\pi}{6} t\right) - \frac{\pi}{6} t \cos \left(\frac{\pi}{6} t\right)$

Now, what's left is to find the velocity of the object at time $t = 2 s$
For that you substitute the value t for 2.

You'll see that the answer is what I have given up there. But you might have to solve it further on yourself.