Reaction time : the lapse of time between stimulation and the beginning of response.


    Would you like to measure your reation time?
    Would you like to estimate how fast you can drive safely on the highway?



     You are driving on the high way and listening to the music you like most.

     Suddently, you see the brake light of the car in front of you just turned on.

     You will try to hit the brake and slow down your car.

     But, there is a small time delay before you really do that--- your reaction time.

     During that period of time, your car is still moving at the same HIGH speed!

     If you do not want something VERY BAD happened,

     What is minimum diatance between front of your car and the rear of the car before yours?

     If both cars need the same distance to fully stopped, the miniuum distance =  ( the velocity of your car )* ( your reaction time )

[color=blue][b]New version of this simulation[/b][/color]:  [url=http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=387.0]Reaction time measurement[/url]



















Let's Assume: you are driving a car with speed v, and your reaction time is T[sub]react[/sub].
When you find out something happened, you need time T[sub]react[/sub] to react (including time to hit the brake and time for the brake system to work).
Before the brake really start, the car already move another distanace D[sub]react[/sub]=v*T;
Assume the reaction is 0.8s (it is 0.6-1.0 for ordinary person. The reaction time will be longer if someone has been drinking or who is sick or tired).
For a car moving with speed 72 km/hr (which is equal to 20 m/s), it means that the car move another distance D[sub]reaction[/sub]=20*0.8=16m before the brake is activated. And it will take more time to stop the car (from v to 0).

Now. I am going to show you how to calculate the distance required for the car to be fully stopped.
The friction force between tries and the road is the only external force to slow down the car.
All the energy of the car goes to tires during the process of stopping the car (so the temperature of tires goes up).
Auusume the friction coefficient is ?, then the friction force fr=-?*N =-?*m*g where m is the mass of the car and g is the gravity. (? is between 1-1.2 for ordinary tire and normal road condition. If it is raining, the friction coefficient can be reduced to less than 0.6, and it could be reduced to 0.2-0.4 for ice road condition).

From Newton's law F=m*a = -?*m*g so a=-?*g is the de-acceleration.
So the time for the car to stop T[sub]brake[/sub]=v/|a| = v/(g* ?).
During the above time interval, the speed reduced from v to zero linearly.
the average speed = (0+v)/2 =v/2
So, the braking distance  D[sub]brake[/sub]=average speed * T[sub]brake[/sub]= (v/2) * v/(g* ?)=v[sup]2[/sup]/(2*g* ?)

What is the meaning of the above equation?
It tell us that the stopping distance is proportional to [b]square[/b] of the driving speed.
If the speed is changed from 100 km/hr to 120 km/hr, the distance to fully stop the car change from d[sub]100[/sub] to (144/100)*d[sub]50[/sub]=1.44 *d[sub]100[/sub].

For the above case, v=72km/hr (45 mile/h)=20m/s.  (g=9.8 m/s[sup]2[/sup] and I wil use g=10 m/s[sup]2[/sup] to simply the estimation, ?=1 is used)
D[sub]brake[/sub]=v[sup]2[/sup]/(2*g* ?)= 20[sup]2[/sup]/(2*10*1)=20 m

The driver need T[sub]react[/sub] to react and the car need T[sub]brake[/sub] to be fully stopped, which imply the total distance traveled is equal to  D[sub]react[/sub] + D[sub]brake[/sub] = v*T[sub]react[/sub] + v[sup]2[/sup]/(2*g*u).

For car at v=108 km/hr (67 mile/h) = 30 m/s :
D[sub]react[/sub]= 30*0.8=24 m
D[sub]brake[/sub]= 30*30/ (2*10*1)=45m
So, the car need 24+45=69m to fully stopped.
This is a very long distance (assume the length of the car is 3m, it is a distance of 23 cars in a line).

If several cars with the same speed are in line in high way, the minimum distance between cars is D[sub]react[/sub]. Because all the car need the same distance to fully. (recommend: multiple D[sub]react[/sub] by 1.5 as safty factor).

However, if you are driving on a road, and someone jump into the road from the sideway.
The car need D[sub]stop[/sub]=D[sub]react[/sub]+D[sub]brake[/sub] to fully stopped.
It is the same if a car accident happened in front of you.
All the cars within D[sub]stop[/sub] from the accident will bump into each other.

Please estimate your own reaction time and calculate D[sub]react[/sub]+D[sub]brake[/sub] for the maximum speed you normally drive in the high way. May be you will drive slower after you have calculated the value.

The police might not be there to give you a ticket when you drive too fast.
Nature law require D[sub]react[/sub]+D[sub]brake[/sub]=v*Treact+v[sup]2[/sup]/(2*g*u) for a car to fully stopped.
You will alway receive ticket if you violate the NATURE LAW.
(You might be lucky if you were sent to hospital instead of ...).