Finding displacement+distance from a v-t graph

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In summary, when looking at a velocity-time graph, the area under the graph represents displacement. However, distance is not the same as displacement and can be found by integrating to create a distance-time graph. If the equation of the graph is not given, distance can be estimated by calculating the changes in distance for each interval and adding them together.
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Homework Statement


This is just a general question. When you have a velocity-time graph, I know that the area under the graph is the displacement. How about the distance? It's not the same as the displacement value, is it?


Homework Equations


n/a


The Attempt at a Solution


I'm stumped. I don't even know if it's possible to find distance, since velocity is a vector and distance is a scalar value.
 
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  • #2
You should be able to integrate to form a distance/time graph. Distance is not the displacement. If I walk 10 feet to the right, 5 feet to the left, 5 feet to the right, and 5 feet to the left, my displacement is only 5 feet to the right. The total distance I traveled is however 25 feet. If you calculate the changes in distance for each interval of increasing/decreasing, and add up the absolute value of those, you should get the total distance. It helps that the function you have is v/t, in that, you can simply solve it equal to zero and find the critical points and use them on the distance/time graph to figure out the distance.
 
  • #3
I see. Is there a way to do it without integration, though?
 
  • #4
The reason why I'm asking about not using integration is because I wasn't given the equation of the graph.
 
  • #5
Without the actual equation, you'll have to estimate as best you can using the graph.
 

1. How do you find displacement from a v-t graph?

To find displacement from a v-t graph, you need to calculate the area under the curve. This can be done by dividing the graph into smaller sections, calculating the area of each section, and then adding them together. The units of displacement will depend on the units of velocity and time used in the graph.

2. What is the difference between displacement and distance on a v-t graph?

Displacement refers to the change in position of an object, while distance refers to the total path travelled by the object. On a v-t graph, displacement can be found by calculating the area under the curve, while distance can be found by adding the lengths of all the segments on the graph.

3. How do you calculate velocity from a v-t graph?

Velocity can be calculated by finding the slope of the v-t graph. This can be done by selecting two points on the graph and using the formula: velocity = (change in velocity)/(change in time). The units of velocity will depend on the units of the v-t graph.

4. Can a displacement on a v-t graph be negative?

Yes, a displacement on a v-t graph can be negative. This indicates that the object has moved in the opposite direction of the positive direction on the graph. For example, if the positive direction on the graph is to the right, a negative displacement would mean the object has moved to the left.

5. How does acceleration affect the v-t graph?

Acceleration affects the v-t graph by changing the slope of the graph. A positive acceleration will result in a positive slope, indicating an increase in velocity, while a negative acceleration will result in a negative slope, indicating a decrease in velocity. The steeper the slope, the greater the acceleration of the object.

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