Position-time graph made with info from a velocity time graph

In summary, the first graph shows a route that travels at a speed of 70 km/h (S) for 5 minutes. After 5 minutes, the velocity increases to 90 km/h (S) and stays at that speed for the next 3 minutes. After 35 minutes, the velocity decreases to 80 km/h (S) for the last 3 minutes of the graph. The second graph shows a route that travels at a speed of 30 km/h (S) for 5 minutes. After 5 minutes, the velocity increases to 90 km/h (S) and stays at that speed for the next 2 minutes. After 30 minutes, the velocity decreases to 80 km/h (S) for the last 2 minutes of the graph.
  • #1
jesstryin
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Homework Statement



I have been given three velocity-time graphs, and have been asked to use the data from these to create position-time graphs. Each graph represent a route that generally goes south. Changes in direction to go east or west and gradual changes in velocity and time to stop at intersections, and so on, have not been included.

To explain the first velocity/time graph:

70km/h (S) traveled for 5 min, then in no time it jumps to 90km/h (S) from t=5 to t=35, then in no time it switches to 80km/h (S) from t=35 min to t=65 min

Homework Equations



I know that distance= time X speed, and velocity is change in position/change in time, so does that mean I use change in position = velocity X change in time?

The Attempt at a Solution



5min = 0.083 hours

V X T = 70km/h (s) X 0.083 h = 5.81 km
So, does this mean that at five minutes on the position-time graph, I mark down 5.81 km as the position? And for the second one:

30 min (from t=5 to t=35) = 0.5 hour
90km/h (s) X 0.5h = 45 km

So, do I mark down the first position as 5.81km and the second position as 45km?

If I did this wrong, please tell me the correct equation and show me how to complete this problem so I can learn, I have been trying to teach myself physics and it is hard, so being shown how to complete this problem would help
 
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  • #2
Yes, that looks right. Another thing to think about when doing these graphs is that since velocity is distance over time, then if you have a position vs. time graph, the slope will be the velocity (i.e. rise over run = position over time). So for example, using the first velocity you could say that the position time graph will have a slope of 70 km/h from 0 to 5 minutes (watch out for units). Doing your calculations gives you the same answer -- this is just another way to think about these problems.
 
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  • #3
Thanks! I am done making the position-time graphs but need help with the rest of the question. They ask me to record the distance for each route. I know distance = speed X time, but I only have the time, not the speed (the velocity is different from speed I think). Can you tell me what equation to use to record the distance, each route has different sections of the trip that are at different constant velocities.

Also, the last part of the question asks me to measure the displacement from Bradford to Milton using a map, then compare the difference between the distances traveled for each route with the displacement I find. I looked it up, and found that the exact distance is 71.6 km, (driving distance is 85 km according to the same map). Would this be the displacement, or am I doing something wrong?

Thanks again for your help I appreciate it :)
 

1. What is a position-time graph?

A position-time graph is a visual representation of an object's position (independent variable) over a period of time (dependent variable). It shows the relationship between an object's position and time.

2. How is a position-time graph created using information from a velocity-time graph?

A position-time graph is created by integrating the velocity-time graph. This means that the area under the velocity-time graph represents the object's displacement, which is then plotted on the position-time graph.

3. What does the slope of a position-time graph represent?

The slope of a position-time graph represents the object's velocity. A steeper slope indicates a higher velocity, while a flatter slope indicates a lower velocity.

4. Can a position-time graph be used to determine an object's acceleration?

Yes, an object's acceleration can be determined by analyzing the curvature of the position-time graph. A more curved graph indicates a changing velocity and therefore, acceleration.

5. How can a position-time graph be used to predict an object's future position?

By analyzing the trend of the position-time graph, it is possible to predict an object's future position. If the graph is a straight line, the object is moving at a constant velocity and the position can be predicted using the equation d = vt, where d is the displacement, v is the velocity, and t is the time. If the graph is curved, the object's future position can be estimated by extrapolating the curve.

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