Give an example of a vertical motion with a positive velocity and a negative acceleration.

b. Give an example of a vertical motion with a negative velocity and a negative acceleration.

a. Sure, imagine a squirrel jumping off a tree branch. As it jumps downwards, its velocity is positive (since it's moving in the positive direction, downwards) and its acceleration is negative (due to the force of gravity pulling it downwards).

b. Picture a rocket coming down towards Earth from outer space. As it descends, its velocity is negative (since it's moving in the negative direction, downwards) and its acceleration is negative (again, due to the force of gravity pulling it downwards).

To find examples of vertical motion with a positive velocity and a negative acceleration, or a negative velocity and a negative acceleration, we need to understand the concepts of velocity and acceleration in the context of vertical motion.

Velocity is the rate at which an object changes its position with respect to time. A positive velocity indicates motion in the upward direction, while a negative velocity represents motion in the downward direction.

Acceleration, on the other hand, is the rate at which an object changes its velocity with respect to time. A positive acceleration indicates an increase in velocity, and a negative acceleration represents a decrease in velocity.

Now let's look at the examples:

a. Vertical motion with a positive velocity and a negative acceleration:
An example of this scenario is throwing a ball upwards and then letting it fall back down. When you throw the ball upwards, it initially has a positive velocity. However, due to the force of gravity acting on it (which creates a negative acceleration), the ball slows down and eventually reverses its direction, resulting in a negative velocity as it falls back down.

b. Vertical motion with a negative velocity and a negative acceleration:
An example of this scenario is dropping an object from a certain height. When you release the object, it starts with a zero velocity (assuming it was initially at rest). As the object falls, its velocity becomes negative because it's moving in the downward direction. At the same time, the acceleration remains negative due to the force of gravity acting on the object as it falls.

In both cases, the positive velocity and negative acceleration are temporary states during the course of the vertical motion.