Question

the driver of a train moving at a speed v1 sights another train at a distance , ahead of him moving in the same direction with a slowrer a speed v2.He applied the brake an gives,a constant retardation 'a' to his train .show that there will be no collision if d>(v1-v2)/2a.

Answer 1

Answer:

Hi ! This is an amazing problem of kinematics ! This also uses some understanding about your ideas in change of frames of references.

Because, the situation is a little bit difficult to observe and analyse the problem from the ground frame, what I'm gonna do is to hop onto the last coach of the train moving with velocity v2 so that now what I see is the train driver just behind me in another train moving at velocity v1-v2 towards me and I'm supposing myself to be stationary, trying not to hit me. I can measure the distance between the end of the my coach and the start of the engine of the second train as 'd'

So, now I want to avoid the mishap and for this we'll have to stop the train just in distance d so that it does not hit me and I'm not going to leave the world.

Thats it !

So, by using the kinematical equation.

0 = (v1-v2)^2 - 2ad

which means, the final velocity of the train should be zero behind me

and, so for that the minimum value of d must be as follows,

d = (v1-v2)^2/2a

And hence, if from t=0 the distance between the train behind me and the last coach of my train is greater than what d I found out, I'm probably gonna be here in the world surviving the mishap !

Hope this helps you ! So you see physics isn't difficult until we analyse and put our life in line for it ! ^_^

Have a great day ! and all the best !

Answer 2

Answer:

${Hey!!}$

• The question is based on the concept of relative velocity.

• As mentioned,

The speed of train A = v1

The speed of train B = v2

• Train B is moving with a slower speed than Train B and it produces retardation.

So, acceleration of train A = - α

acceleration of train B = 0

Now, by using formula :

• v² = u² - 2αs

° v = 0

° u = v1-v2

• 0² = u² - 2αs

• - u² = -2αs

• - (v1-v2)² = - 2αs ( - α = retardation )

• (v1-v2)²/2α = s

OR

• s = (v1-v2)²/2α

• The distance should be more in order to avoid the collision, which proves the above equation.

Hope it helps you ♥️!

@charlie16