## Explanation

### Yes, it means speeding up in the opposite direction of motion

### Detailed Explanation

Negative velocity and positive acceleration can indeed occur simultaneously. Here's what this scenario entails:

When an object has a **negative velocity**, it is moving in the opposite direction to the positive reference direction. For example, if the positive direction is east, then a negative velocity would mean the object is moving west. **Positive acceleration** means that the acceleration vector is pointing in the positive reference direction.

In this situation, the positive acceleration is working against the negative velocity to reduce the object's speed in the negative direction. As a result, the object is **decelerating**, or slowing down, in its initial direction of motion. Eventually, the object may come to a stop and then start moving in the positive direction if the positive acceleration continues to act upon it.

### Mathematical Representation

Consider the following equations:

$\vec{v} = \frac{d\vec{x}}{dt}$Where $\vec{v}$ is the velocity and $\vec{x}$ is the position vector.

$\vec{a} = \frac{d\vec{v}}{dt}$Where $\vec{a}$ is the acceleration vector.

In this case:

$\vec{v} < 0 \quad \text{and} \quad \vec{a} > 0$### Graphical Interpretation

A graph of velocity versus time for this scenario would show the velocity starting from a **negative value** and approaching zero. The slope of the velocity-time graph represents acceleration, which would be positive:

As $\vec{a} > 0$, the slope will be positive, indicating that the velocity is increasing in the positive direction, or decreasing in the negative direction.

### Conclusion

Thus, having a **negative velocity** with a **positive acceleration** indeed means that the object is **slowing down in the opposite direction of motion**.