(c) What is the approximate maximum velocity of the car? The approximate minimum velocity?

Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015
1st Edition
ISBN:9781680331141
Author:HOUGHTON MIFFLIN HARCOURT
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Chapter10: Radical Functions And Equations
Section: Chapter Questions
Problem 15CT
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Question
Part C
The graph shows the position s = f(t) of a car t hours after 5:00 P.M. relative
to its starting point s = 0, where s is measured in miles.
(a) Describe the velocity of the car. Specifically, when is it speeding up and
when is it slowing down?
(b) At approximately what time is the car traveling the fastest? The slowest?
(c) What is the approximate maximum velocity of the car? The approximate
minimum velocity?
V it can swing UWII!
(b) The car is traveling the fastest at t = hour(s).
(Round to the nearest grid line as needed.)
The car traveling the slowest at t =
hour(s).
(Round to the nearest grid line as needed.)
(c) The car's maximum velocity is
The car's minimum velocity is
V
VI
[24,28]
(Simplify your answer. Type your answer in interval notation. Round to the nearest grid line as needed. Use a
comma to separate answers as needed.)
A
AI
Vi
(1,1)
As
400-
320-
240-
160-
8
80-
0-
0
4
8 12 16
More
G
Transcribed Image Text:The graph shows the position s = f(t) of a car t hours after 5:00 P.M. relative to its starting point s = 0, where s is measured in miles. (a) Describe the velocity of the car. Specifically, when is it speeding up and when is it slowing down? (b) At approximately what time is the car traveling the fastest? The slowest? (c) What is the approximate maximum velocity of the car? The approximate minimum velocity? V it can swing UWII! (b) The car is traveling the fastest at t = hour(s). (Round to the nearest grid line as needed.) The car traveling the slowest at t = hour(s). (Round to the nearest grid line as needed.) (c) The car's maximum velocity is The car's minimum velocity is V VI [24,28] (Simplify your answer. Type your answer in interval notation. Round to the nearest grid line as needed. Use a comma to separate answers as needed.) A AI Vi (1,1) As 400- 320- 240- 160- 8 80- 0- 0 4 8 12 16 More G
Expert Solution
Step 1

The slope at any point in the position-time graph represents the instantaneous velocity of the object under observation in this situation a car.

s = f(t)Instantaneous velocity, v = dsdt = f'(t)

f'(t) also represents the tan(θ) where θ is the angle that the tangent to the curve at that point makes with the x-axis.

Therefore, the more the value θ, the more will be instantaneous velocity at that point.

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