A position vs time graph (velocity graph) and a few questions that go with it

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SUMMARY

This discussion focuses on analyzing a position vs. time graph representing the velocity of a baby crawling between two parents. Key questions include calculating the baby's acceleration at t = 1 minute, determining the times of direction change, finding the baby's location at t = 10 minutes, calculating average velocity over the interval [0,15], and identifying the time(s) when the baby is furthest from the starting point. The graph's critical points are (0,0), (7,5), (10,5), (12,-10), and (15,0), with the x-axis representing time in minutes and the y-axis representing velocity in ft/min.

PREREQUISITES
  • Understanding of calculus concepts such as derivatives and integrals.
  • Familiarity with velocity-time graphs and their interpretation.
  • Knowledge of basic graphing techniques and coordinate systems.
  • Ability to perform calculations involving average velocity and acceleration.
NEXT STEPS
  • Learn how to calculate derivatives from velocity-time graphs.
  • Study the concept of integrals to find distance traveled from velocity data.
  • Explore the relationship between position, velocity, and acceleration in physics.
  • Practice solving similar problems involving motion graphs and calculus.
USEFUL FOR

Students studying physics, particularly those focusing on motion analysis, as well as educators looking for examples of velocity-time graph applications in calculus.

smileyfacer50
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Homework Statement


This graph depicts the velocity (measured in ft/min) of a baby crawling back and forth between two parents (suppose they are sitting on the x-axis) for the first fifteen minutes of a lengthy crawl. Use this graph to answer the following questions, using correct units.

1. What was the baby's acceleration at t = 1 minute?
2. Assuming that the baby began its trek at the origin at exactly 9:10AM, at what time(s) did the baby change direction? Your answer(s) should be exact times, including seconds if appropriate.
3. Assuming again, that the baby started at the origin, give the location of the baby at t = 10 minutes.
4. Give the average velocity of the baby on the interval [0,15]. Show how you used calculus to find your solution.
5. At what time(s) is the baby the furthest from its starting point? Explain your answer using calculus.


Homework Equations



The points given on the graph are: (0,0) , (7,5) , (10,5) , (12,-10) & (15,0) The graph goes up between (0,0) and (4,15). Down from (4,15) to (7,5). Flat from (7,5) to (10,5). Down from (10,5) to (12,-10). Up from (12,-10) to (15,0). The x-axis goes by 1s and is from 0 - 15. The y-axis goes by 5s and is from -15 to 15.
The graph cross the x-axis at about 10 minutes at 45 seconds and again at 15 minutes.


The Attempt at a Solution


I didn't know where to start for any of them...
 
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welcome to pf!

hi smileyfacer50! welcome to pf! :smile:

hint: acceleration is the derivative of velocity, so on a velocity-time graph, it's the … ?

distance is the integral of velocity, so on a velocity-time graph, it's the … ? :wink:
 

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