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

In summary, the conversation discusses a graph depicting the velocity of a baby crawling between two parents for fifteen minutes. The conversation poses several questions related to the graph, including the baby's acceleration at a specific time, the times when the baby changes direction, the baby's location at a specific time, and the average velocity of the baby on the given interval. The conversation also mentions using calculus to find solutions to these questions.
  • #1
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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  • #2
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:
 

What is a position vs time graph?

A position vs time graph is a visual representation of an object's position (y-axis) in relation to time (x-axis). It shows how the position of an object changes over a period of time.

How do you interpret a position vs time graph?

To interpret a position vs time graph, you can look at the slope of the line. A steeper slope indicates a higher velocity, while a flatter slope indicates a lower velocity. The direction of the line also indicates the direction of motion - a positive slope indicates motion in the positive direction, while a negative slope indicates motion in the negative direction.

What is the difference between a position vs time graph and a velocity graph?

A position vs time graph shows an object's position in relation to time, while a velocity graph shows an object's velocity in relation to time. In other words, a position vs time graph shows how far an object has moved, while a velocity graph shows how fast the object is moving.

What does a horizontal line on a position vs time graph indicate?

A horizontal line on a position vs time graph indicates that the object is not moving (i.e. its position is not changing over time). This means that the object has a velocity of 0.

How can you calculate an object's velocity from a position vs time graph?

You can calculate an object's velocity by finding the slope of the line on the position vs time graph. This can be done by finding the change in position (y-axis) divided by the change in time (x-axis) between two points on the graph.

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