Continuity Over an Interval

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Continuity in open interval and closed interval

Continuity in interval , Continuity at point function , Limit based continuity questions, Important points

It magnitude of average speed and average velocity over an interval of time are same, then

Find the average value I_(m) of alternating current intensity over time interval from 0 to (pi)/(omega)

If magnitude of average speed and average velocity over a time interval are same, then

Explain clearly, with ezamples, the distaintion between : (a) magnitude of displacemnt (sometimes called distance ) overand interval of time, and the total length of the path coverd by a particle over the same interval. (b) magnitude of average velocity over an intercal of time , and the average speed ocer the same interval. [ Average speed of a particle over an interval of time is defined as the toal path length divided by the time intrval]. Show in both (a) and (b) that the second quantity is either greater than or equal to first. When is the equality sing true ? [ For simplocity, consider one- dimensional motion only]

Assertion: The magnitude of average velocity of the object over an interval of time is either smaller than or equal to the average speed of the object over the same interval. Reason: Path length (distance) is either equal or greater than the magnitude of displacement.