To find: Find the model for the position function.
Answer to Problem 55E
The model for the distance is
Explanation of Solution
Given information:
Given that the initial velocity was
The model for the velocity is given as
The table for the distance and time is given below:
t | 0 | 0.1 | 0.3 | 0.5 | 0.7 | 0.9 | 1.1 |
s | 0 | 0.07 | 0.22 | 0.36 | 0.49 | 0.60 | 0.71 |
t | 1.5 | 1.7 | 1.9 | 2.1 | 2.3 | 2.5 | 2.7 |
s | 0.89 | 0.97 | 1.05 | 1.11 | 1.17 | 1.22 | 1.25 |
t | 2.9 | 3.1 | 3.3 | 3.5 | 3.7 | ||
s | 1.28 | 1.30 | 1.31 | 1.32 | 1.32 |
Calculation:
In order to find the position, function the given velocity function can be written as:
Integrate the above equation:
Apply the initial conditions
Substitute the value of
This is the required model.
Given that the total coasting distance is 1.32 m.
Substitute
Substitute the value of
The scatter plot of the above data is given below:
Chapter 6 Solutions
AP CALCULUS TEST PREP-WORKBOOK
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