Velocity of a Ball Thrown into the Air The position function of an object moving along a straight line is given by s = f(t). The average velocity of the object over the time interval [a, b] is the average rate of change of f over [a, b]; its (instantaneous) velocity at t = a is the rate of change of f at a. A ball is thrown straight up with an initial velocity of 96 ft/sec, so that its height (in feet) after t sec is given by s = f(t) = 96t − 16t2. (a) What is the average velocity of the ball over the following time intervals? [4, 5] ft/sec [4, 4.5] ft/sec [4, 4.1] ft/sec (b) What is the instantaneous velocity at time t = 4? ft/sec (c) What is the instantaneous velocity at time t = 5? ft/sec Is the ball rising or falling at this time? rising falling (d) When will the ball hit the ground? t = sec