An arrow shot straight up from ground level with an initial velocity of 128 feet per second will be at height h(x) = -16x2 + 128x feet at x seconds.
(a) Determine the velocity of the arrow when x = 0, 1 and 2 seconds.
(b) What is the velocity of the arrow, v(x), at any time x?
(c) At what time x will the velocity of the arrow be 0?
(d) What is the greatest height the arrow reaches?
(e) How long will the arrow be aloft?
(f) Use the answer for the velocity in part (b) to determine the acceleration, a(x) = v '(x), at any time x.