Question

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`?

Answer 1

`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`