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