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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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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.
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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