Why Does Zero Integration of a Velocity-Time Graph Not Confirm Return to Origin?

[The_Engineer]

Say you have a v-t diagram for the motion of a particle in one dimension where the velocity is positive at first and then negative later. If you integrate and get zero, why doesn't that mean that the particle started moving and then came back to the origin?

 

[Andrew Mason]

If a particle undergoes multiple phases of motion (ex. accelerating, then decelerating, then constant acceleration, etc..) then how can you determine where the particle's final position is?

I'm imagining a v-t diagram and if you get the area under all of the velocity curves then you get the total displacement, but not the final position (the particle may have been moving backwards...) How do you get the final position?

Let's keep it simple and apply this only to one dimension.


EDIT: Does integrating the absolute value of all the velocity equations yield total displacement while just integrating yields the final position?

Are we to assume that all motion is in one dimension?

If the particle is moving backwards the velocity will be negative so the change in displacement during that period, ∫vdt, will be negative.

Displacement is the distance from the origin with its direction from the origin (ie. + or - x). The change in displacement is defined as the final displacement (position) minus the initial displacement .

AM

 

[The_Engineer]

Are we to assume that all motion is in one dimension?

If the particle is moving backwards the velocity will be negative so the change in displacement during that period, ∫vdt, will be negative.

Displacement is the distance from the origin with its direction from the origin (ie. + or - x). The change in displacement is defined as the final displacement (position) minus the initial displacement .

AM

Yes, assuming that the motion is in one dimension, does an integral of zero of a v-t curve indicate that the particle has traveled back to the origin or hasn't moved at all?

 

[Dale]

It has traveled back to its starting point, which may or may not be the origin.

 

[sophiecentaur]

Say you have a v-t diagram for the motion of a particle in one dimension where the velocity is positive at first and then negative later. If you integrate and get zero, why doesn't that mean that the particle started moving and then came back to the origin?

Has anyone actually suggested it doesn't?