Finding displacement+distance from a v-t graph

[5.98e24]

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.

 

[QuarkCharmer]

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.

 

[5.98e24]

I see. Is there a way to do it without integration, though?

 

[5.98e24]

The reason why I'm asking about not using integration is because I wasn't given the equation of the graph.

 

[Redbelly98]

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