Yes, acceleration can be positive and negative because acceleration is a vector. It has both direction and magnitude. The direction is what makes it positive or negative. Negative acceleration is usually called deceleration.
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Positive acceleration ==> speeding up Negative acceleration ==> slowing down
positive acceleration is when things speed up; negative acceleration is when things slow down; and zero acceleration is when things do not speed up or slow down, this is called constant speed, or no change in velocity.
If it is gravitational acceleration then it it is positive in downward and negative in upward direction..if it is not gravitational acceleration then it is depending upon the value of acceleration.
A period of constant positive acceleration;a second period of zero acceleration; a third period of constant negative acceleration.
The acceleration is in the direction of the positive force so you will have deceleration in the direction of the negative force.