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The wheels lock and the friction between them and the road is constant for most of the time
When all forces are equal an object is either stationary or moving at a constant speed. Although the car is moving, there is an equal amount of force pushing it backwards there is just a constant force moving it forward. The moment that you apply the breaks, the force pushing the car back exceeds the one pushing forward causing the car to slow rapidly, however this force eventually decreases to equal it's opposite as the backwards force is the friction caused by the opposing movement - therefore it will eventually equal the opposite reaction.