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Finding displacement+distance from a v-t graph

  1. Sep 10, 2011 #1
    1. The problem statement, all variables and given/known data
    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?

    2. Relevant equations

    3. 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.
  2. jcsd
  3. Sep 10, 2011 #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.
  4. Sep 10, 2011 #3
    I see. Is there a way to do it without integration, though?
  5. Sep 10, 2011 #4
    The reason why I'm asking about not using integration is because I wasn't given the equation of the graph.
  6. Sep 11, 2011 #5


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    Staff Emeritus
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    Without the actual equation, you'll have to estimate as best you can using the graph.
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