Velocity, average velocity, uniform velocity, variable velocity, instantaneous velocity

Let us discuss the definitions of velocity, uniform velocity, average velocity, variable velocity and instantaneous velocity

Velocity: The time rate of change of position of a body in a particular direction is known as its velocity.

Or

The time rate of change of displacement of a body is known as its velocity.

i.e.                                            Velocity = displacement/time

Velocity is a vector quantity. It can be positive negative or zero as displacement can be +ve, -ve or zero.

Units of velocity: Units of velocity are the same as those of speed.

i.e.                                            cm s-1 In the CGS system

And                                          ms-1 In the MKS system or SI units

Average velocity: Suppose a body is moving along a straight line (say along x-axis). Let

Displacement of the body in time t1 =

Displacement of the body in time t2 = x1

Displacement of the body in time t2 – t1 =  x2

The value of x2 – x1 depends upon the time interval (t2 – t1)

Let t2 – t1 = dt and  x2-x1= dx

Now, average velocity of a body is defined as the ratio of the linear displacement of the body to the time taken in undergoing this displacement.

Uniform velocity: A body is said to be moving with uniform velocity if its average velocity between any two points along its path is the same in magnitude as well as direction.

Or

A body is said to be moving with uniform velocity is it always moves in the same direction and covers equal distances in equal intervals of time, however small these intervals may be.

Variable velocity: A body is said to be moving with variable velocity if its average velocity is different between different points along its path either in magnitude or in direction or both in magnitude as well as direction.

Or

A body is said to be moving with variable velocity if it covers distances in unequal intervals of time or unequal distances in equal intervals of time, however small these intervals may be, or it changes its direction of motion.

Instantaneous velocity: When a body is moving with variable velocity, then its velocity at a particular instant of time or at a particular point along its path is known as its instantaneous velocity. It is equal to the limiting value of average velocity  as dt tends to zero.

Instantaneous velocity is equal to the differential coefficient of displacement w.r.t time.

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