Suppose that a 1000 kg car is traveling at 25 m/s. its brakes can apply a force of 5000n. what is the minimum distance required for the car to stop?

The car's kinetic energy is

                             (1/2) (mass) (speed)²

                       =    (1/2) (1,000 kg) (25 m/s)²

                       =      (500 kg)  (625 m²/s²)

                       =        312,500 joules .

THAT's the work the brakes have to do in order to stop the car.
They have to absorb that kinetic energy and send it somewhere.

Work done by the brakes = (force) x (distance)

             312,500 joules  =  (5,000 N) x (distance)

                     Distance  =  (312,500 joules) / (5,000 N)

                                   =     62.5 meters .

The brakes soak up the car's kinetic energy, turn it to heat,
and let it blow away in the wind.

Too bad you paid good money to buy that energy in gasoline,
and it ended up blowing away in the wind.  You could have 
stayed home, and just opened some windows and let some
money blow away while you ate chips and watched TV.