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

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