Re: Does stopping slowly or stopping quickly in a car wear out brakes quicker?

It depends on a number of things.  First, let us look at what happens when 
you stop slowly.
If you have front disc brakes, with rear drum brakes (a very common 
situation), the front brakes do all of the braking work.  The reason for 
this is simple.  It takes about 0.4 bar (6 psi) to apply a typical front 
disc brake, since there is no return spring and only a rubber seal ring 
that needs to be moved to start braking.  It takes about 6 bar (90 psi) to 
apply most rear drum brakes.  Drum brakes have return springs to keep the 
brake shoes in place.  They also have springs that hold the shoes to the 
backing plate.  Until the brake line pressure exceeds 6 bar, only the 
front disc brakes operate.  Therefore, there is no wear of the rear brakes 
at all.  Unless the front brakes are quite hot, a gentle brake application 
will wear the brake linings at a very low specific rate (typically, 60 
mg/MJ or 0.005 cubic inches per hp-hour).

Other factors to consider when stopping slowly are the frictional losses 
from the tires, chassis, and air drag.  These help slow the vehicle.  With 
an automatic transmission, the engine will actually increase the braking 
work at low vehicle speeds.

Now let us consider a hard brake stop.  Both front and rear brakes will 
operate, but about 70% of the frictional work will be done by the front 
brakes.  Front brakes do more work because they are more heavily loaded, 
especially with the weight transfer from a hard stop.  The specific wear 
rates will be almost the same as before, but now the rear brakes are 
working.  In addition, the friction losses from the tires, chassis, and 
air drag now are much smaller, on a percentage basis.  The result is that 
the front brakes wear a little less, and the rear brakes wear more on the 
hard stop.  The total brake lining wear (front and rear brake linings) is 
about 20% more for the hard brake stop--using our initial assumptions and 
again assuming the brakes are not hot.

If a vehicle has four-wheel disc brakes (or even four-wheel drum brakes), 
then there will be some wear of the rear brakes--even for light brake 
applications.  The total brake lining wear will again be slightly higher 
for hard brake stops, by about 20% or so.

People that brake hard often also accelerate quickly and use their brakes 
more often.  If this gets the brakes hot, then the brake lining wear rates 
may increase--up to a factor of a hundred times above cool brake wear 
rates.  With hot brakes, the hard brake stops will result in significantly 
more brake lining wear.  Hard braking causes a greater temperature rise 
during the brake stop.  This, in turn, causes higher wear rates for the 
hot brakes.

A few brake lining formulations wear faster when cool, and lightly loaded, 
compared with hotter, and more heavily loaded.  One example is the semi 
metallic brake lining, also called semimet.  These use steel wool and 
other ferrous material, along with graphite, all bound by a phenolic 
resin.   The reason these materials wear so differently is that they 
transfer brake lining material to the disc brake rotor during the initial 
part of a hard brake stop, and then transfer it back to the brake lining 
at the end of the stop.  This back and forth brake lining transfer makes 
semimet brake linings have unusual wear characteristics, compared with 
most other brake lining materials.  A few racing brake linings also behave 
this way.  However, the vast majority of all brake linings behave as 
described in the earlier paragraphs.

Unfortunately, there are no good reference sites on the Internet to add to 
this description.  I hope this was sufficient to answer your question.