Written Homework 7 Solutions

occurs when v(t) = 3 cos(t) = 0 or when t = π
. Thus the maximum distance is
2
3 sin( π
) = 3 · 1 = 3 inches.
2
(c) How fast is the ball going when it is at the midpoint of the track? Does it ever go
faster than this? How can you tell?
Solution: The first time the ball is in the center of the track after it has started
to move is when d = 3 sin(t) = 0 which occurs when t = π. The speed at t = π is
|v(π)| = |3 cos(π)| = |3 · (−1)| = | − 3| = 3, so the speed of the ball at the midpoint
of the track is 3 inches per second which is the maximum speed.
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