Motion Under Gravity                                                                                     

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The motion of an object under the influence of gravity is a typical example of uniform acceleration.

Case 1 Falling Objects

Lets consider  a body drop from height h with an intial velocity u=0 and accelerates uniformly downward under gravity  with acceleration  due to gravity g , then cover distance s=h in time t, when its velocity reaches a final value v. 

then

applying the first equation of motion

     ................ First Equation

u =0

therefore 

when s=h then

Height =

Applying the second Equation

............. Second Equation

u=0 and a=g

Applying the third equation

u=0 and a=g  and s=h

therefore

Applying the fourth equation

s=h u=0 a=g

therefore

Case  2  Objects throw upwards

Lets consider  a body throw upward to height h with an intial velocity u and decelerates uniformly  under gravity with a =-g  then cover distance s=h where h is the final height in time t, when its velocity reaches a final value v=0. 

applying first equation

Applying second equation

v=0 and a=-g

0=u-gt

Applying third equation

  v=0,  a=-g  and s=h

Applying fourth equation

s=h, a=-g

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