DISPLACMENT, DISTANCE, SPEED, VELOCITY AND ACCELERATION

Displacement:
Shortest distance between two points is called displacement 
                                                              OR

The displacement is a change in the position of body form its initial position to final position


Unit:
 SI unit of displacement is metre (m)                   

Dimension:

            The dimension of displacement is [L]
VELOCITY:
The time rate of change of displacement is known as velocity. It is a vector quantity. Its direction is along the direction of displacement. Mathematically, average velocity can be written as                   
 Its SI unit is ms-1 and its dimensions are [LT-1]

Uniform Velocity:

If a body covers equal displacements in equal intervals of time, it is said to be moving with uniform velocity.

Variable Velocity:

            If a body covers different displacements in equal intervals of time then body is moving with variable velocity.

Note:   Whenever the average and instantaneous velocities are equal the body moves with uniform velocity.

Instantaneous Velocity:

            If the velocity of the body is not uniform then instantaneous velocity of the body to be measured. It is defined as:

            The velocity of the body measured at any particular instant of time.”

                                                                                             

read as limiting value of  approaches zero.

If the instantaneous velocity does not change, the body is said to be moving with uniform velocity.

Acceleration:

            The time rate of change of velocity of the body is called acceleration. Mathematically 

As velocity is a vector so any change in velocity may be due to change in its magnitude or a change in its direction or both.

Average Acceleration:

Consider a body whose velocity changes from to in a short interval of time ∆t as shown in fig(a). the average acceleration during the time interval is given.                                                                                             

                                                                                                        

Since velocities and change in velocity is a vector quantity, therefore, acceleration is also a vector quantity.

Units:

            Units of acceleration are m/sec2 and dimensions are [LT-2]

Uniform Acceleration:

            If the velocity of the body changes uniformly in equal intervals of time, however, short the interval may be, then acceleration is said to be uniform e.g.

            The uniform acceleration in practical life is the acceleration due to gravity (g). Its value is 9.8 m/sec2in vertically downward direction.

Variable Acceleration:

            If the change in velocity in equal interval of time is not equal or direction of the velocity changes then acceleration is called variable or non-uniform acceleration.

Instantaneous Acceleration:

            It is the acceleration of a body at a particular instant. In average acceleration if the time interval ∆t is so small that it approaches to zero, then we get instantaneous acceleration as
                           

Note: When a body moves with uniform acceleration, then its average and instantaneous acceleration are always equal.

Positive Acceleration:

If the velocity of a body is increasing then its acceleration is positive.

Negative Acceleration:

            If the velocity of a body is decreasing, then its acceleration is negative. The negative acceleration is also called retardation or deceleration.