The Formulae

Oh, come on. It’s not that bad.

There are only two of them, and the first one you already know, or could work out for yourself.

Velocity

Or as noted previously, “speed”.

• Our speed over any period will be our initial speed plus the increase in speed due to acceleration.

If you are driving at 30 Km/h and press the accelerator pedal slightly, your speed will increase gently up to a certain point, and then stay there.

Each second of constant pressure on the accelerator will increase your speed by a fixed amount.

You can see this on modern cars that have a dial for “revs” or engine revolutions.

If you keep the “revs” at, say, 2,500 rpm, your speed will increase in a steady, linear fashion.

The formula is:

v=u+at

Literally: Final velocity (v) is the starting, or initial, velocity (u) plus the acceleration (a) multiplied by the time (t).

We are interested in stopping the car, rather than increasing its speed, so for us our initial velocity is expressed as “Final Velocity”, and since we want to come safely to a dead stop, that final velocity will be zero. Mph or Km/h or fps.

Which leaves us with 0=u+at.

We know the acceleration, we called it “Braking Acceleration”.

If our velocity is 88 fps and our (braking) acceleration is 20 fps/sec, then the time taken to stop will be 88/20, or about four-and-a-half seconds.

Providing that we know our Braking Acceleration, we can calculate the time it will take us to come to a complete stop from any given velocity; it is a simple exercise in division.

Distance

A little, but not a lot, more complicated.

If we are traveling at 88 fps for ten seconds, we will travel 880 feet. That seems obvious.

But what if we are accelerating (or braking, which is just negative acceleration)?

You can think of the distance traveled under acceleration as being the average of distance traveled at the start of the accelerating period and the distance traveled at the end of the period, all added up.

The formula is ½ * a * t^2.

You can read that as “A half ay tee-squared”, or “A half of the acceleration multiplied by the square of the time”.

Putting them together we see:

s = ut + ½ at2

By similar reasoning to that in the preceding section, we are interested in stopping the car, rather than increasing its speed, so for us our initial velocity is expressed as “Final Velocity”, and since we want to come safely to a dead stop, that final velocity will be zero. Mph or Km/h or fps.

Which leaves us with s= 0t + ½ at2

Or simpler: s= ½ at2

We know the acceleration, we called it “Braking Acceleration”.

If our (braking) acceleration is 20 fps, then the distance traveled in coming to a complete stop will be ½ multiplied by 20 multiplied by 4.4 squared, or about two hundred feet.

Providing that we know our Braking Acceleration, we can calculate the TIME it will take us to come to a complete stop, and hence we can calculate the DISTANCE we will travel in coming to a complete stop.

It’s time for a revelation.

A Revelation

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