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
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:
Two bodies are moving in opposite directions at speed V1
& V2 respectively. The relative speed is defined as Vr=V1+V2
Two bodies are moving in same directions at speed V1
& V2 respectively. The relative speed is defined as Vr=|V1−V2|