For each of the following velocity vs. time graphs try to sketch what you think the corresponding position-time graph will look like. Then try to sketch the corresponding acceleration-time graph. Be prepared to present and justify your results. 1. 2. 3.
For each of the following velocity vs. time graphs try to sketch what you think the corresponding position-time graph will look like. Then try to sketch the corresponding acceleration-time graph. Be prepared to present and justify your results. 1. 2. 3.
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Transcribed Image Text:Lesson 4: A Qualitative Look at Rates
By considering specific velocity-time functions of the motion of a particle as rate of
change functions and then trying to draw 1) a rate of change function of the rate of
change function and 2) a function that "undoes" the given rate of change function. Of
course, we are talking about creating the acceleration-time function and the position-time
functions, respectively, when supplied with a velocity-time function. It is assumed that
you have some conceptual knowledge of the derivative as a rate of change function and
the definite integral as an accumulation function. As you work through Exploration 4.1,
try to reconcile both the physical aspects and the mathematics theory behind your
answers.
Exploration 4.1: A Qualitative Look at Rates
Work with gaining a qualitative understanding of graphs of functions. In particular focus
on the relationships between acceleration, velocity, and position vs. time in terms of rates
of change of the functions given.
For each of the following velocity vs. time graphs try to sketch what you think the
corresponding position-time graph will look like. Then try to sketch the corresponding
acceleration-time graph. Be prepared to present and justify your results.
1.
2.
5.
14
3.
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Step 1: Determine the given data:
VIEWStep 2: 1) Understand the velocity time graph:
VIEWStep 3: 1) Draw the position time and acceleration time graph:
VIEWStep 4: 2) Understand the velocity time graph:
VIEWStep 5: 2) Draw the position time and acceleration time graph:
VIEWStep 6: 3) Understand the velocity time graph:
VIEWStep 7: 3) Draw the position time and acceleration time graph:
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