#### Physics (NTSE/Olympiad)

# 1. Motion

__Equation of Motion__

** Motion under uniform acceleration** **(a) 1**^{st} Equation of MotionConsider a body having initial velocity 'u'. Suppose it is subjected to a uniform acceleration 'a' so that after time 't' its final velocity becomes 'v'. Now we know,

or

** v = u + at ** …..(i)

**(b) 2**^{nd} Equation of Motion Suppose a body has an initial velocity 'u' and uniform acceleration 'a' for time 't' so that its final velocity becomes 'v'. The distance travelled by moving body in time 't' is 's' then the average velocity = (v + u)/2.

Distance travelled = Average velocity × time

s =

**s = ut + at**^{2} … … (ii)

** (c) 3**^{rd} Equation of Motion Distance travelled = Average velocity x time

s =

……(iii)

from equation (i)

, we have

Substituting the value of t in equation (iii), we get

2as = v

^{2} – u

^{2} or

**v**^{2} = u^{2} + 2as … . (iv) The equations of motion under gravity can be obtained by replacing acceleration by acceleration due to gravity (g) and can be written as follows :

When the body is coming towards the centre of earth

**(a) v = u + gt **

(b) h = ut + gt^{2}

(c) v^{2} = u^{2} + 2ghWhen a body is thrown upwards with some initial velocity, then a retardation produced due to attraction of the earth. In equations of motion, a is replaced by (–g) and thus equations become.

**(a) v = u – gt **

(b) h = ut – gt^{2}

(c) v^{2} = u^{2} – 2gh

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