### Time Distance and Speed

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Some basic formulae:

·          Speed = distance/time

·         Time = distance /speed

·         If the speed of a body changed in the ratio of ”a:b” ,the time taken changes in the ratio  “ b:a” .

·         X km/hr   = (X)×(5/18)      meter/second

·         X meter/second  =    (X)×(18/5)      km/hr

Some theorems:

Theorem 1 : if a certain distance is covered at  x km/hr and same distance is covered at y km/hr then average speed during the whole journey is given by     = 2xy/(x+y)  km/hr.

Applications : this theorem is generally used in equal distance kind of problem. Like a student goes to school at a certain speed and returns to his home a  different  speed. Then his average speed can be calculated  by this method.

and thus the distance between his school to home can also be calculated.

Theorem 2 : if travelling at a certain speed a man reaches his workplace ‘x ’  minutes early and if he travels on another speed , he reaches  ‘y’ minutes late then distance between his house to office is given by

Required distance = (product of two given speeds / difference of two given speeds )   ×   difference between arrival times in hours .

Theorem 3 : : if travelling at a certain speed a man reaches his workplace and returns at  a different a different speed , if the whole journey took ‘x’ hours to complete the journey then

Required distance = (product of two speeds / addition of two speeds)    ×   (total time taken in hours )

Note : the time is always taken according to speed, as if speed is given in km/hr then time will also be taken in hours.

Theorem 4: if two persons A and B start at a the same time in opposite directions from two points and after passing each other they complete the journeys in ‘a’ and ‘b’ hrs respectively  then

A’s speed : B’s speed  = √b  : √a

·Theorem 5: speed and time are taken inversely proportional   therefore                        S1T1 = S2T2= S3T3

Where S1, S2 , S3 are speeds and  T1, T2, T3 are times taken to travel the same distance.( while the distance is remains fixed or constant.)

Concepts of relative speeds:

Case 1:

Two bodies are moving in opposite directions at speed V1

& V2 respectively. The relative speed is defined as Vr=V1+V2

Case 2:

Two bodies are moving in same directions at speed V1

& V2 respectively. The relative speed is defined as Vr=|V1−V2|

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