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 128 ft/sec, so that its height (in feet) after t sec is given by s = f(t) = 128t - 16t².
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 128 ft/sec, so that its height (in feet) after t sec is given by s = f(t) = 128t - 16t².
Chapter3: Polynomial Functions
Section3.5: Mathematical Modeling And Variation
Problem 7ECP: The kinetic energy E of an object varies jointly with the object’s mass m and the square of the...
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![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 128 ft/sec, so that its height (in feet) after t sec is given by
s = f(t) = 128t - 16t².
(a) What is the average velocity of the ball over the following time intervals?
[4, 5]
[4, 4.5]
[4, 4.1]
(b) What is the instantaneous velocity at time t = 4?
ft/sec
ft/sec
ft/sec
ft/sec
(c) What is the instantaneous velocity at time t = 7? (To determine this, find the AROC over smaller and smaller intervals
until the ROC is clear.)
ft/sec
Is the ball rising or falling at this time?
rising
falling
(d) When will the ball hit the ground?
t =
Submit Answer
sec](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffaa3be14-7f82-4920-95bd-32284dc4e75b%2F3255cf69-07b8-4795-8b23-70922509c75a%2Fbgo8n7_processed.png&w=3840&q=75)
Transcribed Image Text: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 128 ft/sec, so that its height (in feet) after t sec is given by
s = f(t) = 128t - 16t².
(a) What is the average velocity of the ball over the following time intervals?
[4, 5]
[4, 4.5]
[4, 4.1]
(b) What is the instantaneous velocity at time t = 4?
ft/sec
ft/sec
ft/sec
ft/sec
(c) What is the instantaneous velocity at time t = 7? (To determine this, find the AROC over smaller and smaller intervals
until the ROC is clear.)
ft/sec
Is the ball rising or falling at this time?
rising
falling
(d) When will the ball hit the ground?
t =
Submit Answer
sec
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