# Prove 2 cars moving on same road will not have Collision

• ag35cosy
In summary, the conversation discusses a problem involving two cars traveling at the same velocity on a highway. The cars must decelerate to a lower velocity when approaching a tunnel, and the problem is to show that the cars cannot collide in this scenario. The speaker suggests drawing a graph to better understand the problem and expresses difficulties in formulating the idea mathematically. They also mention that the conversation may be more suited for the Homework forum.
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...

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.

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.

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.

Danger said:
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.

## 1. How do you prove that two cars moving on the same road will not have a collision?

The most common way to prove this is by using the laws of motion and the principles of relative motion. By calculating the velocities and trajectories of the two cars, it can be shown that they will not intersect at any point on the road.

## 2. What factors contribute to the probability of a collision between two cars on the same road?

Factors such as the speed and direction of the cars, the distance between them, the road conditions, and the reaction time of the drivers can all affect the likelihood of a collision. These variables must be carefully considered when determining the probability of a collision.

## 3. Can two cars moving on the same road ever collide?

In theory, it is possible for two cars to collide on the same road. However, with proper traffic laws and safe driving practices, the chances of a collision are greatly reduced. It is important for drivers to follow traffic rules and maintain a safe distance from other vehicles to prevent accidents.

## 4. How does the concept of inertia play a role in proving that two cars on the same road will not collide?

Inertia is the tendency of an object to resist changes in its motion. In the case of two cars on the same road, their inertia will keep them moving in their respective directions unless acted upon by an external force. This means that if both cars are moving at a constant velocity and direction, they will not collide.

## 5. Can technological advancements help prevent collisions between two cars on the same road?

Yes, advancements in automotive technology such as automatic braking systems, lane departure warnings, and adaptive cruise control can greatly reduce the chances of a collision between two cars on the same road. These systems use sensors and algorithms to detect potential collisions and intervene to prevent them from happening.

Replies
6
Views
1K
Replies
9
Views
1K
Replies
4
Views
2K
Replies
9
Views
4K
Replies
30
Views
2K
Replies
335
Views
10K
Replies
1
Views
1K
Replies
60
Views
1K
Replies
10
Views
1K
Replies
36
Views
2K