Asmall ball is fastened to a long rubber band and twirled around it such a way that the ball moves in an elliptical path given by the equation r(t) = i 4b cos(wt) + j 3b sin(wt), where b and w are positive constants. (

Given that a small ball is fastened to a long rubber band and twirled around it such a way that the ball moves in an elliptical path given by the equation
,
where b and are positive constants.

a) The velocity of the ball v as a function of time t is given by
.

b) The speed of the ball v = |v| as a function of t is given by
.

c) The speed v at t = 0 at which time the ball is at its maximum distance from the origin is given by
.

d) The speed v at at which time the ball is at its minimum distance from the origin is given by
.

e) The acceleration of the ball, a, as a function of t is given by
.

f) The magnitude of the acceleration of the ball
.