How does an object's position and velocity change as the object accelerates

Explanation:    

Velocity describes how the position changes and acceleration describes how the velocity changes.

If someone is accelerating, it means that he is speeding up or if someone is accelerating, it also means that he is speeding down.

In the slowing down case, the acceleration is in the opposite direction of the velocity. If the car's driver applies a break then there will be a negative acceleration. The velocity of the car decreases here. Then the position of the object will also get change.

In the speeding up case, the acceleration is in the same direction of the velocity. If the car's driver starts his car or accelerates his car then there will be a positive acceleration. The velocity of the car increases here. Then the position of the object will also get change.