Train Formulas

Conversion:

km/hr to m/s conversion:

m/s to km/hr conversion:

Formulas for finding Speed, Time and Distance 

1.     Time taken by a train of length l metres to pass a pole or standing man or a signal post is equal to the time taken by the train to cover l metres.
 
 
2.     Time taken by a train of length l metres to pass a stationary object of length b metres is the time taken by the train to cover (l + b) metres.
 
 
3.     Suppose two trains or two objects bodies are moving in the same direction at u m/s and v m/s, where u > v, then their relative speed is = (u - v) m/s.
 
 
4.     Suppose two trains or two objects bodies are moving in opposite directions at u m/s and v m/s, then their relative speed is = (u + v) m/s.
 
 
5.     If two trains of length a metres and b metres are moving in opposite directions at u m/s and v m/s, then:
 

Time taken by the trains to cross each other=

 
 
6.     If two trains of length a metres and b metres are moving in the same direction at u m/s and v m/s, then:

Time taken by the faster train to cross the Slow Train=

7.     If two trains (or bodies) start at the same time from points A and B towards each other and after crossing they take a and b sec in reaching B and A respectively, then:
      (A's speed) : (B's speed) = (b : a)

Example sum

1) A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?
Speed = [ 60 * (5 / 18 ) ] m/sec
= ( 50 / 3 ) m/sec
Length of the train = ( Speed * Time )
= [( 50/3)*9 ] m= 150m



2) A train 125 m long passes a man, running at 5 km/hr in the same direction in whichthe train is going, in 10 seconds. Find the speed of the train?
Speed of the train relativeto man = ( 125 /10 ) m/sec
= ( 25 / 2 ) m/sec
= [(25/2) * ( 18/5) ] km/hr
= 45 km/hr
Let the speed of the train be x km/hr.
Relative speed = (x - 5 ) km/hr.
(x-5)=45
x = 45+5x 
= 50 km/hr

Basic Formulas

If two trains of p meters and q meters are moving in same direction at the speed of x m/s and y m/s ( x > y ) respectively then time taken by the faster train to overtake slower train is given by = [ (p + q)/ (x -y)]

Example sum

3)Two trains of equal length are running on parallel lines in the same direction at 46 km/hr and 36 km/hr.The faster trainpasses the slower train in 36 seconds.Find the length of each train?
Let the length of each train be x metres.
Distance covered = 2x metres.
Relative speed = ( 46 - 36 ) km/hr
= [ 10*(5/18) ] m/sec
= ( 25/9) m/sec
=  ( 2x/36) = ( 25/9)
= 2x=100  
 x = 50
Basic Formulas

If two trains of p meters and q meters are moving in opposite direction at the speed of x m/s and y m/s respectively then time taken by trains to cross each other is given by = [ (p + (x + y)]


Example sum

4) Two trains of equal lengths take 10 seconds and 15 seconds respectively to cross a telegraph post. If the length of each train be 120 metres, in what time (in seconds) will they cross each other travelling in opposite direction?
Speed of the first train = ( 120 / 10 )m/sec
= 12 m/sec
Speed of the second train = ( 120 / 15 )m/sec
= 8 m/sec
Relative speed = ( 12 + 8 )
= 20 m/sec  
Required time = [ ( 120 + 120 ) / 20 ] sec
= 12 sec