# The position of an object moving along a line is given by p(t) = 2t - sin(( pi )/6t) . What is the speed of the object at t = 4 ?

Apr 9, 2016

Speed at t = 4:
$v = 2.26 m . {s}^{- 1}$

#### Explanation:

If we are given position as a function of time, then the function for speed is the differential of that position function.

Differentiate p(t):
• Differential of $a \sin \left(b t\right) = a b \cos \left(b t\right)$
v(t)=(dp(t))/(dt) = 2 - π/6cos(π/6t)

Now substitute in the value of t to find the value of speed at that time (t = 4):
v(4) = 2 - π/6cos(π/6× 4) = 2.26 m.s^(-1)