Question

How do you find the distance travelled from t=0 to `t=2pi` by an object whose motion is `x=cost, y=sint`?

Answer 1

`2 pi` units

Explanation:

That is circular motion about a unit circle, a complete cycle happens in period `t = 2 pi`. So the distance is the circumference of the unit circle `= 2 pi cdot 1`.

As it's labelled a calculus question, if you want to do an an arc length calculation, then:

`int_0^(2 pi) sqrt((dot x)^2 + (dot y)^2) dt`

`= int_0^(2 pi) sqrt((- sin t)^2 + (cos t)^2) dt`

`= int_0^(2 pi) dt = 2 pi`