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Distance Time and Speed

Relation between time distance and speed 

Relation between time distance and speed  is given by the equationsSpeed=Distance/Time
          or
Distance=Speed*Time
          or
Time=Distance/Speed
Unit of speed is km/hr or m/s
If speed is given in km/hr,then inorder to convert it  in to m/s multiply by 5/18
1km/hr=5/18m/s
If speed is given in m/s,then inorder to convert it  in to km/hr multiply by 18/5

Ratio of speed

  • If ratio of speed of two moving object is a:b, then ratio between times taken for covering same distance is b:a. 
  • If two objects A and B moving in opposite direction from two different places reach at common point in t1 and t2 hrs respectively ,Then Speed of A:Speed of B=sqrt(t2/t1)

Average speed 

  • average speed=total distance/total time taken.
  • If a moving object covers a certain distance with a speed of x km/hr and again covers same distance with a speed of ykm/hr, then average speed is 2xy/(x+y).
  • If a moving object covers a certain distance with a speed of x km/hr and again covers same distance with a speed of ykm/hr and again with zkm/hr,then average speed is=3xyz/(xy+yz+xz)

Points to be noted while doing 'train and time' problems

  • If two trains are travelling in same direction ,then their relative speed is equal to difference of their speeds.Then Time taken by the fast train to cross the slower train is =Sum of lengths of both trains/difference of their speed 
  • If two trains are travelling in opposite direction ,then their relative speed is equal to sum of their speeds.Then time taken to pass one another is =Sum of lengths of both trains/sum of their speed. 
  • when a train is clearing a pole or a point, then distance covered by train is equal to its length 
  • When a train is covering a platform or bridge or tunnel ,then distance covered by train is equal to sum of the length of train and the length of platform/tunnel/bridge. 
  • When a moving train crosses another train, then distance covered is equal to sum of lengths of both trains. 

Boat and stream problems

  • If speed of stream=xkm/hr and speed of boat in still water is ykm/hrthen speed of boat in downstream=x+y km/hr ,speed of boat in upstream=y-x km/hr 
  • If speed of boat in upstream and speed of boat in down stream is given then, speed of boat in still water=1/2(speed in upstream+speed in downstream) , speed of stream=1/2(Speed in downstream - speed in upstream)
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