Winter 1998

A student wrote:

My second question: How could acceleration be + or - independent of whether v is + or -? When you say: + acceleration, do you mean acceleration on the + direction, or do you mean the object is accelerating in either direction-- + or -? Also, when you say - acceleration, do you mean deceleration, or acceleration on the negative direction? Same type of question goes with velocity.

Prof. Seidler responds:

I am going to answer your question in the context of 1-dimensional motion. When one says that the acceleration is positive, this means that the acceleration is in the positive-direction as defined by the chosen coordinate system. Conversely, a negative acceleration means only that the accceleration is in the negative direction (as defined by the chosen coordinate system). Consider the following cases of motion in the vertical direction, assume that 'up' is positive.

1. You have just tossed a ball straight up into the air. The ball is still moving upward, so its velocity is positive, but its acceleration is negative.
2. The ball has now reached its highest point. The velocity is (instantaneously) zero, but the acceleration is still downward (i.e. negative).
3. The ball has passed its highest point, and begun to fall. Now the velocity is negative and the acceleration is (still) negative.