The Facts

Car Length

More correctly, “vehicle length”, but we’ll make this initial exploration easier at the start by assuming there are just 4-wheeled cars on the road. We know that trucks and buses exist, but we’ll solve for them once we have established our formula for cars.

I will be using a car length of twelve feet. Yes, that’s 12.

Yes, I know that your car is shorter, but his car is longer, and I have to start somewhere.

If you have downloaded the spreadsheet you’ll see that I have keyed in “12” alongside “vehicle length”. You can key in whatever value you want. Later on we’ll key in “40” for passenger coaches and “70” for 18-wheeled tractor-trailers.

Driver Reaction Time

(Saturday, February 07, 2026: Driver reaction time is the period between thr retina of the eye issuing a signal, and the muscles beginning to move. In our example " the muscles beginning to move" is the event of lifting the foot OFF the accelerator pedal and moving it TO the brake pedal. I suppose that this time must lie between 0.5 and 1.0 seconds; we should add that to the initial driver reaction time. That is use a value between 1.7 and 2.2 seconds)

I will use 1.2 seconds as the time between the driver’s eyes accepting some photons and the signals being transmitted from the brain to “tighten the grip on the steering wheel” in readiness for the next command which is probably “stamp the foot on the brake pedal” or even “wrench the steering wheel to the right/left”.

Yes, I know that you reaction times are better, and that he is distracted with the radio, or the ham and cheese sandwich.

But we have to start somewhere. Again, you can make changes as you do your own calculations.

Braking Acceleration

I’m going to go with thirty feet per second per second, or 30 fps/sec. Why? I know that 60 miles per hour is 88 feet per second. I think that I might be able to slow down to a complete stop by braking from 60 mph to zero mph in about three seconds. That’s 20 mph/second, or about 20 fps/second.

I’ve seen figures on the web of 10 meters per second per second, but web pages about braking distance tend to be written by technical nerds, like me, so those pages are probably discussing high-performance systems.

But we have to start somewhere. Again, you can make changes as you do your own calculations.

Velocity Or Speed

Velocity is speed-with-distance, and we will be considering traveling in a straight line along a lane of a road or highway, so we can use the terms interchangeably. Newtonian equations always refer to “velocity”, so we will use that term when discussing formal values.

In particular, for our empirical solution we will test different speeds ranging from zero to 80 mph in increments of 5 or 10 mph.

The Formulae

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