Question

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 144 ft/sec, so that its height (in feet) after t sec is given by s = f(t) = 144t − 16t2.

What is the average velocity of the ball over the following time intervals?

(a) [4, 5] ft/sec

(b) [4, 4.5] ft/sec

(C)[4, 4.1] ft/sec

Answer 1

we are given equation for position as

(a)

we can use formula

interval is [4,5]

now, we can plug value

..........Answer

(b)

we can use formula

interval is [4,4.5]

now, we can plug value

..........Answer

(C)

we can use formula

interval is [4,4.1]

now, we can plug value

..........Answer