Question

What is the instantaneous velocity of an object moving in accordance to `f(t)= (sint,cost^3)` at `t=pi/2`?

Answer 1

`vec v = -(3pi^2)/4sin(pi^3/8)vec i_y`

Explanation:

`{(dotx = cost),(doty=-3t^2sint^3):}`

For `t= pi/2`:

`{(dotx = 0),(doty=-(3pi^2)/4sin(pi^3/8)):}`

So the instantaneous velocity is directed along the `y`-axis:

`vec v = -(3pi^2)/4sin(pi^3/8)vec i_y`