We now arrive at the second way of looking at this problem. Let us assume that we have good brakes, so that the braking process is limited not by the interaction between the pads and disks but by the interaction between the tyres and the ground. In other words, let us assume that our brakes are better than our tyres. To keep things simple and back-of-the-envelope, assume that our tyres will give us a constant deceleration of

The time t required for braking from speed v can be calculated from: t = v / a which simply follows from the definition of constant acceleration. Given the time for braking, we can calculate the distance x, again from the definitions of acceleration and velocity:

Remembering to be careful about converting miles per hour to feet per second, we arrive at the numbers in Table 1.

Table 1: Times and Distances for barking to zero from various speeds

We can immediately see from this table (and, indeed, from the formulas) that it is the distance, not the time, that varies as the square of the starting speed v. The braking time only goes up linearly with speed, that is, in simple proportion.

The numbers in the table are in the ballpark of the braking figures one reads in published tests of high performance cars, so I am inclined to believe that the second way of looking at the problem is the right way. In other words, the assumption that the brakes are better than the tyres, so long as they are not overheated, is probably right, and the assumption that brakes dissipate energy at a constant rate is probably wrong because it leads to the conclusion that braking takes more time than it actually does.

My final advice to Mark was to leave lots of room. You can see from the table that stopping from 210 mph takes well over a quarter mile of very hard, precise, threshold braking at 1g!