VELOCITY

“Rate of change of displacement:

Vector so may be + , - , zero ,

Unit: meter/sec , km/hr , cm/sec etc

Dimensional formula: [LT-1]

 condition Þ Direction of velocity and displacement must be same

Example: There are four persons are standing at the four corners of a square. Assume that all four persons start with Constant

speed v and move towards each other. Find the time when all four persons will meet to each other. If length of each side is given l.

Solution:

AC2 = AB2 + BC2

= l2 + l2

 

 

Now for person A direction of V

Component of v along direction of displacement is v  

 

Note: General result for above Concept

Trick: If there is n person and polygon of n sides then time require to meet each other

 

Example. If there are 6 persons moving towards each other with Constant speed v. Initially all 6 persons standing at the Corner

of a hexagon then time required to meet

Solution: Use above result for general Case

 

 

Note: Similarly if there are three persons standing at the corners of a equilateral triangle.

 

MEAN OR AVERAGE VELOCITY

 

Case I Same time (S.T.)

Now (Vav) AtoC = ?

 

 

 

 

 

As above

l1 = V1 t

l2 = V2t and l3 = V3 t

 

 

 

 

Case II Same gap (S. G.)

Now (Vav) AtoC = ?

          

 

 

 

 

Now Case I (S.T.) + Same gap (S.G.)

Example   

Solution: Now for B to D Same gap

 

 

Acceleration:

“Rate of change of  velocity  

Vectors, so may be + , - , zero

Unit : met/sec2

Dimensional formula [LT-2], 

Case I : Acceleration due to change in magnitude of velocity

If magnitude of velocity is increasing Þ

If magnitude of velocity is decreasing Þ

Retardation or Deceleration

Case II : Acceleration due to change in direction of velocity 

 

 

 

 

 

Example: A car is moving with 10 m/s due north after 2 second it take left turn and keep moving with 10m/s due west. Acceleration the Car will be       

  

  

  c 52m/s2 due S-E

 d 52m/s2 due S-W            

Solution:

Initial velocity V1=10j m/s    

Final Velocity V2=-10i m/s  

Due North – West direction

a=V2-V1∆t  

=-10i-10j2  

a= -5i-5j  

a=52 m/s2  

                                           Answer is (d)

For direction of acceleration  

Ans 52 m/s2S-Wdirection                                                                

CONVERSION OF GRAPH

SOME IMPOSSIBLE (NON REALISTIC) GRAPH

(1) Distance never decrease

(2) Time never constant never decrease

 

(3) At a time no multiple values