Instantaneous velocity ,acceleration and relative velocity

Instantaneous velocity:

(i) The velocity of a body at any particular instant in its journey is known as  Instantaneous velocity

(iii) Unit of instantaneous velocity m/s

(v) If the particle is in uniform motion along a straight line,  Average velocity  =   Instantaneous velocity

Acceleration:

(i)  The rate of change of velocity of a body is called acceleration

(iii) The direction of acceleration lies along the direction of change in velocity

Uniform  acceleration :

(i)  If the average acceleration over any time interval equals the instantaneous acceleration at any instant of time, then the acceleration is said to be uniform or constant. It does not vary with time. The velocity either increases or decreases at the same rate throughout the motion

Retardation:   

(i) The negative acceleration is known as retardation

(ii)  Anybody travelling with decreasing velocity possesses retardation or deceleration

Unit of retardation: m/s²

Example problem:

A bullet moving with a speed of 150ms^-1 strikes a tree and penetrtes 3.5cm beforestopping. What is the magnitude of its retardation in the tree and the time taken for it to stop after striking the tree?

(A) Given, Initial speed U=150m/s,    Final speed V=0m/s,

Relative velocity:

(i) Velocity of one body with respect to that of another body is called relative velocity

(ii) The velocity of `A` with respect to that of `B` is given by 

(iii) If ‘A’ and ‘B’ are moving at an angle  with one another, then,   velocity of `A` with respect to that of `B` is given by  

Example Problem:

Two parallel rail tracks run north-south. Train A moves north with a speed of 54Kmh^-1 and train B moves south with a speed of 90Kmh^-1. What is the (a) Velocity of B with respect to A?  (b) Velocity of ground with respect to B?