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 144 ft/sec, so that its height (in feet) after t sec is given by s = f(t) = 144t – 16t2.
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
![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 144 ft/sec, so that its height (in feet) after t sec is given by
s = f(t) = 144t - 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, 4.1]
|-1.44
X ft/sec
(b) What is the instantaneous velocity at time t = 4?
16
ft/sec
(c)
What is the instantaneous velocity at time t = 8?
ft/sec
Is the ball rising or falling at this time?
O rising
falling
(d) When will the ball hit the ground?
t = |0
X sec](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F22542f52-fc18-4f9b-90f3-86db01220e87%2F1f9df03d-321b-4327-a939-f5cba6cbf237%2F1r220aa_processed.png&w=3840&q=75)
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