(a) Given that the position of an object is x(t) = A cos (t, show that vx(t) = − (A sin (t. [Draw the velocity vector for point P in Fig. 10.17b and then find its x - component.]
(b) Verify that the expressions for x(t) and vx(t) are consistent with energy conservation. [Use the trigonometric identity sin2 w t + cos2 (t = 1.]