Question

The graph of position in time is: r(t)=(t-sint)i+(1-cost)j with t equal to or bigger than 0. Find the maxim and minimal values of |v| and |a|.

I kown a have to take derivative of r(t) to find v(t) and the darivative of v(t) to find a(t). v(t)= (1-cost)i+(sent)j a(t)=(sint)i+(cost)j and |v(t)|=sqrt(2-2cost), the minimal value will be when cost is -1, so it will be sqrt(4). But my teacher solved and doesnt considered the sqrt, and write the answer like 4, and not 2. Why?

Answer 1

looks like cycloid

Answer 2

yes it is cycloid

Answer 3

but why my teacher doesn't considered the square root, if the module is square root of 2-2(-1)?

Answer 4

yes ... differentiate and take square root of the squares, that gives you the value at which you will have minimum |v(t)|