Linear Equations

Third equation motion:- The third equation of motion can be obtain by elimination t b/w the first  two equations of motion.

From the 2nd equation of motion we have
                 
                 s =   ut + ½ at2 -------------------(1)
                   And the first equation of motion
                     v = u + at

this can be rearrange and written as
                         at = v – u
                         t= (v- u) /2
 

putting this value of t in equation

s = u( v –a)/a + ½ a [ (v-u )/a ] 2  and finally we get
                      
v2 = u2 + 2as --------------- (a)

where  v = final velocity

u = initial velocity
a = acceleration
s = distance

Note:-  we should remember that

  1. if the body starts from the rest, its initial velocity, u = 0
  2. if a body comes to rest (it stop) its final velocity, v = 0
  3. if a body moves with uniform velocity its acceleration, a = 0

uniform circular motion:- when a body moves on a circular path this motion is called circular motion.

 In other words

When a body in circular path with uniform speed its motion is called uniform circular  motion.

Examples :

  1. artificial satellite moves under uniform circular motion around the earth.
  2. The moon moves in uniform circular motion around the earth.
  3. The earth moves around the earth in uniform circular motion.
  4. The tip of second hand of a watch exhibits uniform circular motion on the circular dial of the watch.

An athlete moving on a circular track with constant speed exhibits circular motion.

To calculate the speed of a body in uniform circular motion:-

When a body one round of a circular path then it covers a distance equal to its circumference which is equal to 2 πr, where ‘r’ is the radius of the circular path
 

Then
      Speed = 2 π r / t where
v= speed, r = radius of the circular path and t = time taken

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