Final answer:
It is possible to have a negative velocity and positive acceleration, meaning an object is speeding up in the opposite direction of its initial motion.
Step-by-step explanation:
Yes, it is possible to have a negative velocity but a positive acceleration. This scenario would mean that an object is speeding up in the opposite direction of its initial motion, that is, it is accelerating towards the positive direction while moving in the negative direction. The correct answer to your question would be (a) Yes, it means speeding up in the opposite direction of motion. Contrary to common misunderstanding, positive acceleration does not necessarily mean the object is moving in the positive direction, rather, it is moving in the direction of the change in velocity. For instance, if we assume motion to the right along the x-axis is positive, and to the left is negative; if a car is moving to the left (negative velocity) but is accelerating to the right (positive acceleration), it means that the car is speeding up in the opposite direction of its initial leftward motion. It's imperative to realize that acceleration is in the direction of the change in velocity, not always in the direction of motion. Therefore, an acceleration that reduces the negative velocity (speeds the object up in the positive direction) while the object is still moving in the negative direction results in a scenario where you have negative velocity and positive acceleration.