We received a call from a reader about our road-test spec sheets and specifically the emergency-braking tests. He wanted to know how it is possible for the distance to vary while the stopping times appear to be close when comparing the braking performance between different vehicles. It took basic mathematics and the equations of motion stemming from Newton’s second law to explain the apparent discrepancy:
The braking times and distance results from 100-0 km/h are not always proportional. The reason for this is that the deceleration during the braking event of a vehicle is not constant. If the deceleration during the braking events of all cars were constant, a slower time would have always meant a longer stopping distance. Let’s look at two extreme examples compared with a good braking event at constant 1 G (9,81 m/s2) deceleration with a stopping distance of 38,6 metres and a time of 2,8 seconds from 100 km/h.
Example 1: poor braking at high speeds
If the vehicle failed to decelerate for 0,5 seconds at 100 km/h (27,7 metres/second) before the normal 1 G deceleration took place, the figures would have been influenced in this way:
New stopping distance: 38,6 m + (0,5 x 27,7 m/s) = 52,45 m
New time: 2,8 sec + 0,5 sec = 3,3 sec
Example 2: poor braking at low speeds
If the vehicle failed to decelerate for 0,5 seconds at 1 km/h (0,3 metres/second) after the normal 1 G deceleration took place, the figures would have been influenced in this way:
New stopping distance: 38,6 m + (0,5 x 0,3 m/s) = 38,75 m
New time: 2,8 sec + 0,5 sec = 3,3 sec
It’s clear that the same stopping time can result in vastly different distances depending on the variance of deceleration during braking.