# Concept of Relative Speed : Shortcut Tricks on Train

Relative speed is the phenomena that we observe daily whenever two objects are moving simultaneously.

Suppose you are travelling in train an there is second train coming in opposite direction on a parallel track. It seems second train is moving much faster than it actually is.

On the other hand I you are travelling in car and see another car moving besides you, also moving in same direction. The cars when seen form others will seem stationary.

So in this chapter you will need to keep in mind

If two objects are moving in opposite direction their speed should be added.

If two objects are moving in same direction their relative speed should be difference of their speeds.

When the train passes a platform it should travel the length equal to sum of lengths of train and platform.

Example 1 how long does a train 110 m long running at a rate of 36 km/hr take to cross the bridge 132 meters in length?

Here train must travel its own length plus the length of bridge.

36 km/hr= 36 x 5/18= 10 m /sec

Required time= 242/10= 24.2 seconds

Example 2: two trains 121 m and 99 m in length respectively are running in opposite direction, one at a rate of 40 km/hr and other at a rate of 32 km/hr, In what time they will be completely clear of each other from moments they meet?

Relative speed=40+32= 72 km /hr=20m/sec

Required time= Total length / Relative speed

= 121+99/20

=11 sec

Example 3: In same example if train were moving in same direction

Relative speed=40-32= 8 km /sec= 20/9 m/sec

Required time= Total length / Relative speed

= 121+99/20/9

=99 sec

Example 4: two trains of lengths 400 m and 600m have speed of 36 km/hr and 54 km/hr respectively. In what time will the train be able to cross each other’s completely, given that trains are moving in

- The same direction with the faster train approaching the slower
- The opposite directions

When the trains are moving in the same direction, the faster train crosses the slower when the tail of faster just passes the front end of slower trains.

Hence, the distance that the faster train has to cover before crossing the slower train = sum of lengths of the trains = 400m+600m=1000m

Relative speed of faster train with respect to slower train

= (54-36) = 18m/hr

=5m/sec

Therefore, time taken for faster train to cross the slower train= 1000/5=200sec

The distance travelled by the train together= um of the lengths of the two trains

=400m+600m=1000m

Relative speed of trains=

54+36= 90km/hr= 25 m/s

Time taken= 1000/25= 40 sec