a.
To calculate: The velocity and time, acceleration and time of the graph.
a.
Explanation of Solution
Given information:
The graph of the function is as shown below.
Calculation:
Steps to plot velocity time graph.
Calculation of derivative from the points
For the
The
The one point on the derivative of the function is
The table of values with other slopes is shown below.
Time(t) | Velocity(v) |
4 | 62.5 |
8 | 50 |
11.5 | -33.3 |
Graph of the points is as shown below.
Steps to plot velocity time graph.
Calculation of derivative from the points
For the
The
The one point on the derivative of the function is
The table of values with other slopes is shown below.
Time(t) | Acceleration(a) |
6 | -3.125 |
9.75 | -23.86 |
Graph of the points is as shown below.
b.
To plot: The graph of velocity and acceleration.
b.
Explanation of Solution
Given information:
The function is
Calculation:
Steps to plot velocity time graph.
The function is
Differentiate with respect to
The velocity time graph is as shown below.
Steps to plot acceleration time graph.
The function is
Differentiate with respect to
The acceleration time graph is as shown below.
Conclusion: The graph has been plotted and the graphs are same as obtained in part (a).
Chapter 2 Solutions
AP CALCULUS TEST PREP-WORKBOOK
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- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning