Acceleration


Acceleration 
                The rate of change of Velocity is called Acceleration. If a body is moving with initial velocity 'u' after some time final velocity 'v' then
                             Change in Velocity 
 Acceleration =--------------------------------
                                Time taken 
                         Final Velocity(V)- Initial Velocity(U)
                       = ----------------------------------------------------
                                         Time taken 
                          V-U
                  a  =------- 
                           t
S.I.Unit of Acceleration is metre/second2(m/s2).
C.G.S.Unit of Acceleration is centimetre/second2 (cm/s2).
Acceleration is a vector quantity. So, acceleration
two types 
                     1) Negative Acceleration 
                      2) Positive Acceleration 

          Fig: Negativ and Positive Acceleration  

                        A body is moving along straight line an initial velocity 'u' after some time final velocity 'v'. If v>u then we said that the body is moving "Positive Acceleration". If v<u then we said that the body is moving "Negative Acceleration". 

   1) A body moved along straight line an initial velocity 10 kmph after 1hour final velocity 30kmph. Find acceleration of the body?
Solution: u= 10kmph; 
                 v= 30kmph;
                  t= 1h ;
                 a =?
                        v-u
                  a=--------
                           t
                      30-10
                    =---------
                          1
                       20kmph
                     =----------
                          1h
                  a = 20km/h2 (Positive Acceleration)

2) A body moved along straight line an initial velocity 40kmph after 2hours its velocity 30kmph. Find acceleration of the body?
Solution: u= 40kmph;
                  v= 30kmph;
                   t= 2hours;
                   a=?
                      v-u
                 a=-------
                       t
                    30-40
                  =--------
                     2
                   -10
                 =------
                     2
               a =-5km/h2 ( Negative Acceleration)
3)A body moves along straight line an initial velocity 5 metre per second after 3 hours its velocity 18 kmph. What is acceleration of the body?

4) A body moves along straight road, its change in velocity 5kmph during time interval 5hours. What is acceleration of the body?
 These two questions practice for students.
Uniform Acceleration 
             A body is moving along straight line "when the body covered equal change in velocities in equal intervals of time" then we said that the body is moving "Uniform Acceleration". 

Uniform Acceleration

                  Fig:  Uniform Acceleration 

  In the graph  the straight line represents the body moves uniform acceleleration. 

Non-Uniform Acceleration 
                    A body is moving along straight line "when the body covered unequal change in velocities in equal intervals of time or equal change in velocities in unequal intervals of time or unequal change in velocities in unequal intervals of time" then we said that the body is moving "Non-Uniform Acceleration".          
                                  
Non-Uniform Acceleration
                  Fig: Velocity- Time graph  

In the graph curved line represents a body moves Non-Uniform Acceleration. 

Motion with Constant Acceleration along straight line 
                 Let us consider a body is moving along straight line with the velocity at time t=0s be u and the velocity at t=ts be v with contant acceleration 'a'.                                                              
                      Here  Initial velocity =u at t=0s;
                                 Final velocity  =v at t=t s;
                                    Acceleration = a;
                 So,          
                                Change in velocity
                          a=-----------------------------
                                  Change in time
                                v-u
                           a =-----
                                  t
Velocity-Time

                           at=v-u
                            v=u+at-----------> (1)

Position-Time


                                 Total displacement 
Average Velocity=-----------------------------
                                   Total time taken 
                 v+u      s
                 ------  = -----
                  2            t
     (v+u)t =2s
      (u+at+u)t = 2s.        ( From equation ----1)
        ut+att+ut = 2s
         
Equation
            
            

Velocity-Postion


From equation (1)&(2)
                      (v+u)t =2s.     
                (v+u)(v-u)                 (From equation 1)
                --------------   = 2s
                       a       

Equation
Three equations
 
These three equation is called Equation of Motion. 

    
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