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?
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?