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Math
CalculusSingle Variable Calculus: Early Transcendentals, Volume I8th Edition

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Chapter 2.8, Problem 56E
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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

(a) The graph of a position function of a car is shown, where s is measured in feet and t in seconds. Use it to graph the velocity and acceleration of the car. What is the acceleration at t = 10 seconds?

Chapter 2.8, Problem 56E, (a) The graph of a position function of a car is shown, where s is measured in feet and t in

(b) Use the acceleration curve from part (a) to estimate the jerk at t = 10 seconds. What are the units for jerk?

(a)

To determine

To find: The acceleration at t=10 seconds by using the graph of velocity and acceleration of the car.

Explanation

The graph of the position function is given with s in feet and t in seconds.

From the given graph, it is observed that the slope of the position function is always positive for t>0. So, the velocity curve always will have a positive functional value.

The slope of the curve increases very slowly initially, then just before t=10.

The slope of the curve increases very rapidly and then the increase in slope decreases just after t=10.

After the time just before t=20, the slope decreases rapidly.

Graph:

Use the above information and trace the graph of velocity function as shown below in Figure 1.

From Figure 1, it is observed that velocity contains the horizontal tangent at one point

(b)

To determine

To calculate: The jerk at t=10 using the acceleration curve from part (a) and write the units.

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