# 2 second rule true at highway speeds?

1. Sep 24, 2011

### rarouch

Here's the question:

A safe following distance for a car is often described as "two seconds". In
other words, if you pass the same point as the car in front of you two seconds
later, the distance between the cars is safe.
Inquiry: is this rule true at highway speeds?

Parameters:

Car A is in front, car B is behind.
Both are traveling with the same velocity (approx 100 km/h).
There are two seconds between car A and car B.
Car A will commence braking at a rate you will be given later.
Car B will not react for a certain amount of time (given later) and then will
brake.
The rate of car B's braking will be given later.

Question: Can car B stop before it collides with car A?

I was given the question this way. It's basically an evaluation that my teacher will give on a day and I have time to prepare for it. What would be reasonable amounts for the parameters?

My thoughts:
It basically depends on the rate of the braking of the cars. But in general, the car's deceleration will be approximately same and since we can take that the car B driver will react quickly than 2 sec therefore they may not collide but they really depend on the rates, which is why I was wondering, what would be a reasonable breaking rate? and how would I unput that into a formula?

Thank you very much.

2. Sep 24, 2011

### PhanthomJay

Once you know the braking rate (deceleration) of each car, you'll have to use the kinematic motion equations. A car can only decelerate as fast as friction allows; and friction depends on the tire type and road surface conditions. Oh, maybe 6 m/s/s might be an approximate rate on dry pavement, without the tires skidding.

3. Sep 26, 2011

### rarouch

Thank you for the input. What would I have to do if the braking rate for both of the cars are different?

4. Sep 26, 2011

### Phrak

Originally you might assume both cars slow due to braking at the same deceleration.

The hint you need is this:

"Car B will not react for a certain amount of time (given later) and then will brake".

For car B, assume reaction time is constant, independent of velocity, and initially assume 2 seconds reaction time. How is the following-distance to avoid collision a function of the velocities of car A and B?

Last edited: Sep 26, 2011
5. Sep 26, 2011

### PeterO

Good brakes and a dry road would generally give a braking rate of 0.5g or -5 m.s-2.

Given that 100 km/h is just under 30 m.s-1, that means nearly 6 seconds to stop. That means a braking distance of nearly 90m - but both cars take that long to brake so that is not the problem.
It is the reaction distance - the distance covered by the second car while the driver reacts.

If you are 2 seconds behind the car in front, you would be almost 60m behind at highway speed.
A typical reaction time is just under 0.5 seconds.
In that time you will travel ~ 15m. so you should still stop 45 m from the car in front.

If the following car has less efficient brakes, it will be a bit closer.

Note: if the braking efficiency is the same for both cars, the distance behind the car in front needs to be your reaction time at least, so traveling 2 seconds behind allows for your reaction time to be a hopeless 2 seconds.