**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:**

AC^{2} = AB^{2} + BC^{2}

= l^{2} + l^{2}

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 (V_{av}) _{AtoC} = ?

As above

l_{1} = V_{1} t

l_{2} = V_{2}t and l_{3} = V_{3} t

Case II Same gap (S. G.)

Now (V_{av}) _{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/sec^{2}

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**=**V**2**-**V**1**∆t*

*=**-10**i**-10**j**2*

*a**= -5**i**-5**j*

*a**=52 m/**s**2*

**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**