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```        two trains take 3 sec to pass one another when going in the opposite direction but only 2.5 sec if speed of one is increased by 50 %.what would be the time one would take to pass the other when going in the same direction at their original speed ?
plz explain the the process of solving.```
5 years ago

Pallav Agarwal
33 Points
```										Let the speed of 1st train be v.
Let the speed of 2nd train be u.
Let their combined length (distance) be d.
When going in opposite directions with original speeds,
=> (v+u) = d/3
=> d= 3v + 3u..........(1)
When speed of one train is increased by 50 %, v ---> 1.5v
=> (1.5v+u)=d/2.5
=> d = 3.75v + 2.5 u............(2)
=>(2)-(1)
=>0.75v - 0.5u = 0
=>1.5v = u

time = distance/speed
When going in same direction, time= d/(u-v)
Since d = 3v + 3u = 3v + 3*1.5v= 7.5 v
u - v= 0.5v
=> time = 7.5v/0.5v = 15 seconds

```
5 years ago
SKS
40 Points
```										Dear Pallav,
Thank you so much for your answer but i know the solution this way.The twist is that it is the question of RELATIVE MOTION as i have mentioned in the title.so please tell me how to solve it by applying the concept of relative motion.
```
5 years ago
Pallav Agarwal
33 Points
```										Ok, I didnt see that.
The method is still the same, but in examination you would have to add a few lines to the solution.
In the first case, from ground frame,
The first train is moving to the RIGHT with velocity v.
The second train is moving to the LEFT with velocity u.
So, without using direction, we can say if 1st train is moving with velocity v, the second is moving with velocity (-u)<--- NOTICE the NEGATIVE sign.
So velocity of 1st train with respect to 2nd (relative velocity) will be v-(-u)=v+u.
Now you apply the same formula.

In the last case, while moving in the same direction, the velocities will be +v and +u, so relative velocity will be v-u. Apply the method in my first reply to get the answer.

```
5 years ago
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