Graphing Position Versus Time for Accelerated Motion 

Braking is the act of slowing down an object, if you will, it's the reducing of an objects speed.  What braking is not, it's not always a negative acceleration, braking is an acceleration that is in the opposite direction of the motion of the object.  To accelerate (at least how the lay person uses the word) is the act of speeding an object, increasing it's speed. The truth is to accelerate and object is to change the motion of an object, weather it's to speed it up, slow it down, or change it's direction of motion.  So to speed an object is not a question of positive or negative acceleration, it's a question which way the acceleration points compare to it's motion.  If the arrows point in the same direction it's speeding it up, opposite direction it slows it down.  

Slowing down 

Negative velocity

Negative acceleration  

Positive velocity 

Positive acceleration 

Speeding up 

Positive velocity 

Negative Acceleration 

Negative velocity 

Positive acceleration