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 $t = 4$ ?

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Answer 1 · 2016-04-09T11:09:11

Speed at t = 4:
$v=2.26 m.s^(-1)$

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 $asin(bt) = abcos(bt)$
$v(t)=(dp(t))/(dt) = 2 - π/6cos(π/6t)$

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

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