Q: If an object starts at 0 and accelerates to the left to final position 1, why is “a” negative? Is it because the object is going to the left of 0, so it is “negative accelerating?”
A: First, the motion (1-D) is toward the left. The velocity is negative according to the sign conventions. Second, this is a speed-up motion, i.e., the object is accelerating, so the velocity and the acceleration must have a same direction (a same sign in 1-D), as shown in the attached picture. As a result, the acceleration is negative.
