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It is not the force of the brakes that is stopping the car but rather external force of friction between tires and the road. Notice that no matter what the force at the brakes is, the car won't stop if there is no friction there(ie. the road is slippery).

This is an excellent question. Consider the NASA space shuttle. It has brakes, yet the brakes work only on the ground - only while the shuttle is landing. Why?

In space, the brakes have nothing to react against. So, as the questioner suspects, the internal forces of the brakes alone are not sufficient to change the velocity of the space shuttle. But once the shuttle lands, and is rolling down the runway, applying the brakes creates friction between the wheels and the runway. And it is the external force of the runway pushing back against the braking wheels that causes the shuttle to slow down.

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