(a) 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.

An object's velocity can be considered negative or positive depending on the direction of motion.

If we consider a stone that is thrown upwards with an initial velocity, the velocity is considered as positive in magnitude or direction. As the stone moving upwards it started deaccelerating which means a negative acceleration. So the vertical motion of the stone can be considered as positive velocity and negative acceleration.

The velocity or acceleration of a body can be negative or positive depending upon its direction of motion. If the body is moving forward, its velocity can be considered as positive and for the opposite direction, the velocity will be considered as negative velocity.

If we consider a vehicle is moving with a constant speed. If at a certain time, the vehicle takes reverse motion then the velocity of the vehicle can be considered as negative corresponding of the initial motion and at the same time if the vehicle slows down then it can be considered as negative acceleration.

Another example we can take- consider in a bike is moving with an acceleration (positive). Now, if the biker press the brake slowly, the bike will move a little backward and the velocity will be converted into negative and as the bike slows down, the acceleration should be also negative.