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Average velocity [<v>]

If Δx is displacement in time Δt, then average velocity in time interval Δt will be
Here xf and xi are the positions of a particle at time tf and ti (tf > ti), respectively, with respect to a given frame of reference.

Instantaneous velocity (v)

It is the velocity of particle at any instant of time.
Mathematically, 24585.png
  • Since distance  |displacement|, so average speed of a body is equal or greater than the magnitude of the average velocity of the body.
  • No force is required to move the body or an object with uniform velocity.
  • The velocity of a body is positive, if it moves to the right side of the origin. The velocity is negative if the body moves to the left side of the origin.
  • When a body reverses its direction of motion while moving along a straight line, then the distance traveled by the body is greater than the magnitude of the displacement of the body. In this case, the average speed of body is greater than its average velocity.

Time average speed

When a particle moves with different uniform speeds v1v2v3, ..., etc., in different time intervals t1t2t3, ..., etc., respectively, its average speed over the total time of journey is given as:
vav = 24601.png
24607.png = 24613.png

Distance averaged speed

When a particle describes different distances d1d2d3, ... with different time intervals t1t2t3, ... with speeds v1v2v3, ..., respectively, then the speed of particle averaged over the total distance can be given as:
vav = 24629.png
24625.png = 24620.png
If speed is continuously changing with time, then
  • When a particle moves with speed v1 upto half time of its total motion and in rest time it is moving with speed v2, then
  • When a particle moves the first half of the distance at a speed of v1 and second half of the distance at speed v2, then
  • When a particle covers one-third distance at speed v1, next one-third at speed v2, and last one-third at speed v3, then

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