Question

What is an example of a vertical motion with a positive velocity and a negative acceleration?

Answer 1

Throwing or launching an object upwards.

Explanation:

A very simple example would be throwing a ball straight up in the air.

Following the convention that upward is positive and downward is negative, the ball has a positive initial velocity (from the throw) which constantly decreases due to acceleration in the opposite (negative) direction, which is that caused by the force of gravity of the earth pulling down on the ball.

This is true because after the ball leaves your hand, you can no longer provide an acceleration to it. Therefore the only force (of concern) acting upon it is the force of gravity, so that the acceleration of the ball is `-g`. This agrees with Newton's second law.

`vecF_"net"=mveca`

`=>F_g=mg`

Where the force of gravity is in the negative (downward) direction and consequently the acceleration due to gravity is also negative, giving `a_"ball"=-g`.

This would not be the case, for example, with a rocket which is launched upward, because the rocket maintains a thrust force against the force of gravity (and drag, etc.), and therefore has a positive acceleration.