Finding displacement+distance from a v-t graph

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In a velocity-time graph, the area under the curve represents displacement, while total distance traveled is different and must account for all changes in direction. Displacement is a vector quantity, indicating the net change in position, whereas distance is a scalar, summing all movement regardless of direction. To calculate distance from a v-t graph, one can sum the absolute values of the changes in distance during each interval, which may involve estimating if the equation of the graph is unknown. Integration can provide a precise method for calculating distance, but it is not the only approach. Understanding these distinctions is crucial for accurately interpreting motion from velocity-time graphs.
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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


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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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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.
 
I see. Is there a way to do it without integration, though?
 
The reason why I'm asking about not using integration is because I wasn't given the equation of the graph.
 
Without the actual equation, you'll have to estimate as best you can using the graph.
 

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