What would the acceleration-time graph of throwing up a ball look like?

[opticaltempest]

This isn't a homework problem but rather a question I am having a hard time finding an answer to using google.com.

I have a ball in in my hand. I throw it straight up as hard as possible into the air. What would the acceleration-time graph look like as the ball is being accelerated then released by my hand.

I'm having trouble picturing what the acceleration-time graph would look like the instant the ball switches from being accelerated by my hand to being accelerated by gravity? Does it instantaneously change from being a positive acceleration w.r.t. the thrower to being a negative acceleration w.r.t. the thrower?

Where are some good links that would show this graphically?

Thanks

 

[Pyrrhus]

Well as you know it depends whether we are considering air drag too, it could be linear or not. Also it depends on modeling the force you exerted, if it's constant or variable (is there an empirical equation for it?). If it's constant and air drag is neglected there would definately be a discontinuity.

 

[quicknote]

The acceleration-time graph of throwing up a ball would have a few distinct features. Initially, when the ball is still in your hand, the acceleration would be zero as it is not yet in motion. As you throw the ball up, the acceleration would increase rapidly, reaching its maximum value at the point of release.

Once the ball is released, the acceleration would decrease due to the force of gravity acting on it. This would result in a curved line on the graph, with the acceleration decreasing as the ball moves higher and higher.

At the highest point of the ball's trajectory, the acceleration would be zero again, as the ball has reached its maximum height and is momentarily at rest before it starts to fall back down.

As the ball falls back down, the acceleration would increase again, but in the opposite direction (negative acceleration) due to the force of gravity pulling it towards the ground. This would result in a mirrored curve on the graph, with the acceleration increasing as the ball falls closer to the ground.

Eventually, the ball would reach the ground and the acceleration would become zero again as it comes to a stop.

To see a visual representation of this graph, you can search for "acceleration-time graph of a thrown ball" on Google or YouTube. Here is a link to an example: