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

1 Answer
David B.
May 20, 2016

s = 3+(pi sqrt(3))/6 ~= 3.91

Explanation:

The speed of an object is the rate of change of it's position with respect to time - in other words, the magnitude of the derivative of the position with respect to time:

s = | d/(dt)p(t)| = |dot p (t)|

In our case we need to do the derivative of our function:

dot p(t) = d/(dt)p(t) = 3 + pi/3 sin(pi/3 t)

plugging in the time given

dot p(2) = 3 + pi/3 sin(2pi/3) = 3+(pi sqrt(3))/6

Therefore the speed, being the absolute value of this, is the same:

s = 3+(pi sqrt(3))/6 ~= 3.91

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