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Classical Physics by Prof.V.Balakrishnan

Lecture Series on Classical Physics by Prof.V.Balakrishnan, Department of Physics, IIT Madras.

Displacement

The change in position vector of the particle for a given time interval is known as its displacement.

AB = r = r2 - r1

Displacement is a vector quantity and its SI unit is meter.
It can decrease with time.

For a moving particle in a given interval of time
 Distance can be a many-valued function but displacement would be always a single-valued function.
 Displacement can be +ve, -ve or 0 but distance would be always +ve.
 Distance ≥ Magnitude of displacement.
 Distance is always equal to displacement only and only if particle is moving along a straight line without any change in direction

Average speed and average velocity :-
  Average speed and average velocity are always defined for a time interval.

      Average speed (v) = Total distance travelled / time interval
                                    =Δs/Δt

    Average velocity = Displacement / time
                                = Δr/Δt 
                                = r2-r1 / t2-t2

Average speed is a scalar quantity, while average velocity is a vector quantity. Both have the same SI units, i.e., m/s

For a moving particle in a given interval of time
  Average speed can be a many-valued function but average velocity would be always a single-valued function.
  Average velocity can be +ve, -ve or 0 but average speed would be always +ve.

Instantaneous speed and instantaneous velocity
 There are defined for a particular instant. (In physics, instant mean a very small interval which is tends to zero).

   Instantaneous speed, 
                     (v) = lim         v = ds/dt
                           = Rate of change of position
Instantaneous speed is the scalar quantity, while instantaneous velocity is the vector quantity, both having the same SI units, i.e., m/s

v= |v|, i.e., instantaneous speed is always equal to magnitude of instantaneous velocity. 

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