Speed and Velocity

Speed

            A body covered 'd' distance during time  interval t1 to t2. How can we say that the body is covered 'd' distance per time interval t1 to t2 ?  So, we want to relation between distance and time. The ratio of distance to time is equal to one physical quantity is called speed. The rate of change of distance by a body is called speed of the body. Speed is very important transport field.
Speed of a body is measured by device is called "speedometer". We can see speedometer device in vehicles. This device is very useful to drivers for safe driving. Speed has only magnitude and hasn't direction. So, speed is a scalar quantity. 
             
                     Distance covered by a body                 Speed   =  ____________________________
                   Time taken the distance covered 
                        by the body
S.I.Unit of speed is metre per second (m/s). C.G.S.Unit of speed is centimetre(cm/s).
Biggest unit of speed is kilometre per hour(km/h)

Relation between km/h and m/s:
       1km=1000m; 1hour =3600s;
                           1km/h = 1000m/3600s
                                       = 10m/36s
                                       = 5m/18s
                          1km/h =  5/18 m/s         

Velocity
    
           A body covered 'd' displacement during  time interval t1 to t2. The ratio of displacement to time is equal to physical quantity is called velocity.  The rate of change of displacement by a  body is called velocity of the body. Velocity has magnitude as well as direction. So, velocity is a vector quantity. 
                                                                                                              Displacement covered by a body 
 Velocity    =___________________________________
                       Time taken the displacement.                                       covered by the body

S.I.Unit of Velocity is metre per second (m/s).
C.G.S.Unit of Velocity is centimetre per
second(cm/s). Biggest unit of Velocity is km/ h.

Note: Speed is a scalar physical quantity 
          Velocity is a vector physical quantity 

Average Speed
                 A body is moving v1 speed at time t1, v2 speed at time t2 and v3 speed at t3. So, when a body is moving with a variable speed, then the average speed of the body is defined as the total distance travelled by the body per total time taken.
                                                Total distance 
                :. Average Speed=-------------------------
                                                 Total time taken 
         A body travelling between two positions travels first half of the distance with speed v1 and next half of the distance with speed v2. Then
                                          Or
      A body is travelling between two positions A,B. It travels from A to B in the same path with speed v2. Then 
                                            2v1v2
               Average Speed=-----------
                                            v1+v2
         A body travelling between two positions travels with speed v1 for time t1 and then with speed v2 for time t2. Then
                                             v1t1+v2t2
               Average Speed=------------------
                                                 t1+t2
               A body travelling between two positions travels first half of the time with speed v1 and next half of the time with speed v2. Then
                                              v1+v2 
                Average Speed=-------------
                                                   2
              A body travelling between two positions travels for the time intervals t1,t2,t3................tn with speeds v1, v2, v3,........vn respectively. 
                               
                              v1t1+v2t2+v3t3+........vntn
 Average Speed=--------------------------------------
                                t1+t2+t3+t4+..........tn

Average Velocity 
                      Similarly,  Average Velocity of the above body is defined as the total displacement covered by the body per total time taken covered the total displacement by the body. 
                                           
                                    Total displacement  
  Average Velocity=-------------------------------
                                     Total time taken 

Uniform Speed
                         Once you observe Doctors,  Policemen and School children dress. These one group of people wear uniform dress. Similarly uniform speed means constant speed. When a body is moving along straight line then the body covers equal distances in equal intervals of time. Then we said that the body is moving with Uniform Speed. 
Distance- Time graph

                      Fig: Distance-Time 

In the graph the straight line represent a body is moving with Uniform Speed. 

Non-Uniform Speed
                           A body is moving along straight line "when the body covers equal distances in unequal intervals of time or covers 
unequal distances in equal intervals of time" then we said that the body's  moving with "Non-Uniform Speed". 
Distance-Time graph

                      Fig: Distance-Time graph

In the graph the curved line represents a body is moving with Non-Uniform Speed. 

Uniform Velocity 
                              A body is moving along straight line "when the body covers equal displacements in equal intervals of time " then we said that the body is moving with "Uniform Velocity".
 
Displacement-Time graph

                         Fig: Displacement-Time
In the graph the straight line represents a body is moving with Uniform Velocity. 
Non-Uniform Velocity 
                         A body is moving along straight line "when the body covers equal displacements in unequal intervals of time or unequal displacements in equal intervals of time " then we said that the body is moving with              "Non-Uniform Velocity".

                Fig: Displacement-Time graph 

Fig: In the graph the curved line represents a body is moving with Non-Uniform Velocity. 





      
         



Comments

Anaya said…
Cool stuff you have got and you keep update all of us. sales velocity formula
January 16, 2022 at 10:52 AM
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