When a ball is dropped from a state of rest at time t = 0, the distance it has traveled after t seconds is s(t) = 16t2. (a) how far does the ball travel during the time interval [4, 4.5]? 68 ft (b) compute the average velocity over the time interval [4, 4.5]. ft/sec (c) by computing the average velocity over the time intervals [4, 4.100], [4, 4.010], and [4, 4.001], . . , estimate the ball's instantaneous velocity at t = 4. (round your answer to one decimal place.) ft/sec.

Part a)

Part b)

Part c)

Explanation:

Part a)

As we know that displacement is given as

now the displacement in 4.5 s and t = 4 s is given as

now displacement is given as

Part b)

So displacement of the ball in given interval of t = 4.00 to 4.5 s

time interval is given as

average velocity is given as

Part c)

So displacement of the ball in given interval of t = 4.00 to 4.1 s

average velocity is given as

Similarly for time interval t = 4.0 s to t = 4.01 s

average velocity is given as

Similarly for time interval t = 4.0 s to t = 4.001 s

average velocity is given as

so instantaneous velocity is given as

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0.19 m/s and 0.45 m/s