# Average velocity [<v>]

If Î”

*x*is displacement in time Î”*t*, then average velocity in time interval Î”*t*will beHere

*x*_{f}and*x*_{i}are the positions of a particle at time*t*_{f}and*t*_{i }(*t*_{f}>*t*_{i}), respectively, with respect to a given frame of reference.# Instantaneous velocity (*v*)

It is the velocity of particle at any instant of time.

Mathematically,

- Since distance â‰¥ |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

*v*_{1},*v*_{2},*v*_{3}, ..., etc., in different time intervals*t*_{1},*t*_{2},*t*_{3}, ..., etc., respectively, its average speed over the total time of journey is given as:*v*

_{av}=

= =

# Distance averaged speed

When a particle describes different distances

*d*_{1},*d*_{2},*d*_{3}, ... with different time intervals*t*_{1},*t*_{2},*t*_{3}, ... with speeds*v*_{1},*v*_{2},*v*_{3}, ..., respectively, then the speed of particle averaged over the total distance can be given as:*v*

_{av}=

= =

If speed is continuously changing with time, then

- When a particle moves with speed
*v*_{1}upto half time of its total motion and in rest time it is moving with speed*v*_{2}, then - When a particle moves the first half of the distance at a speed of
*v*_{1}and second half of the distance at speed*v*_{2}, then - When a particle covers one-third distance at speed
*v*_{1}, next one-third at speed*v*_{2}, and last one-third at speed*v*_{3}, then