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Consider the following scenario:
A car travelling down a road begins to decelera
Consider the following scenario:
A car travelling down a road begins to decelerate at a constant rate. The speed of the car before decelerating was 78 feet per second.
Choose your own value for the constant deceleration rate of the car based on the scenario above and address the following:
Draw a graph or figure to represent this situation.
Describe how the concepts from this module can be applied in this case.
How many feet does the car travel after two seconds?
Provide another example of a scenario that involves the same concept.
Additional Note:
During this week, we will explore the application of calculus to real-world scenarios involving motion, specifically focusing on deceleration. From the discussion prompt, imagine a car traveling down a road that begins to decelerate at a constant rate from an initial speed of 78 feet per second. You will choose your own value for the constant deceleration rate and use it to analyze the car’s motion. Your task is to draw a graph representing the situation, describe how the concepts from this module can be applied, calculate the distance the car travels in two seconds, and think of another scenario where these concepts might be useful.
This exercise will help you understand how to apply derivatives and integrals to describe and predict the motion of objects. By graphing the car’s speed over time and integrating it to find the total distance traveled, you’ll better understand how calculus models real-world phenomena. We have already explored the relationship between the position function ?(?), velocity function ?(?), and acceleration function ?(?). We have defined those relationships as follows:
?(?)=?′(?)
?(?)=?′(?) or ?(?)=?″(?)
This week, we work our way back to the position function given acceleration and initial conditions. That is, we have the following:
?(?)=∫?(?)??
?(?)=∫?(?)??
Note that the initial conditions given are used to find the value of C, the constant of integration.
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