Question

A cheetah runs along the path such that the displacement vs. time (meters vs. seconds) graph is given by the equation: x(t)=(6/π)sin-1t•cos-1t. What is the instantaneous velocity of the cheetah at the point (1/2, π/3)?

Answer 1

use derivatives of arcsin and arccos
\[\frac{d}{dt}\sin^{-1} t = \frac{1}{\sqrt{1-t^{2}}}\]
\[\frac{d}{dt}\cos^{-1} t = -\frac{1}{\sqrt{1-t^{2}}}\]
Find v(t) = x'(t) , use product rule

Answer 2

Thanks!