Zero velocity A projectile is fired vertically upward and has a position given by s(t) = −16t2 + 128t + 192, for 0 ≤ t ≤ 9.
a. Graph the position function, for 0 ≤ t ≤ 9.
b. From the graph of the position function, identify the time at which the projectile has an instantaneous velocity of zero; call this time t = a.
c. Confirm your answer to part (b) by making a table of average velocities to approximate the instantaneous velocity at t = a.
d. For what values of t on the interval [0, 9] is the instantaneous velocity positive (the projectile moves upward)?
e. For what values of t on the interval [0,9] is the instantaneous velocity negative (the projectile moves downward)?
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