Prove 2 cars moving on same road will not have Collision

[ag35cosy]

Hey Guys I am having trouble figuring out solution to this Problem

2 Autos are moving along a Highway in a straight line with same magnitude of velocity v. The distance between the 2 autos is d. Now both the autos, A and B have to deaccelerate themselves to velocity v' respectively , when they are at a distance D from a Tunnel. (v' is the maximum entering velocity in the Tunnel.) Show that the 2 Autos can not have a collision.


Now what they are trying to say is that suppose there is a point at distance D from the face of a Tunnel . When Car A reaches this point it reduces it's velocity from v to v' ( which is the maximum velocity allowed inside the Tunnel). Then Car B (which was d meters behind Car A) reaches this point and also deaccelerates from v to v'. What we have to show is that during all this the 2 cars cannot collide with each other...

I would really appreciate your help...

 

[epenguin]

I take it you have not trouble seeing this is true. Draw a graph in two parts, vertical co-ordinates distance, top graph distance (from some arbitrary point) of the car A, and below car B, both at the same times t (horizontal axis). That should help you express you intuition in formulae and words. If this is a course exercise to hand in, the graph should be part of it.

 

[ag35cosy]

Well I had this question in my preperation test today.. I can visaulise this. and do believe that the statement is true ( that the 2 cars can never collide in this scenario) but I am having troubles in expressing this intuition in terms of Formulae..

I know that when car A reaches a point where it has to deaccelerate, then distance d between the 2 cars will decrease but this will only happen till car B reaches the same point. (But by then Car A would aready have traveled further even if its a very small distance).

Do you have any suggestion, how to express this Mathmatically.

Thanks for the reply

 

[Danger]

Personally, I'd just take a different road.
Honestly now, this belongs in the Homework forum. That isn't meant as an insult; it's just that questions of this nature have their own very valued space here.

 

[epenguin]

Personally, I'd just take a different road.
Honestly now, this belongs in the Homework forum.

Yes. There doesn't seem practically to be that neat a distinction and I don't personally pay attention if I look at today's posts what forum any of them is in, but this one is clearly that side of any borderline.