Displacement as Function of Time Graph Question

[physicsnobrain]

I'd give you 4 out of 5 for that.

During the object's travel, there is a moment which could be described as <CRUNCH!>. Where is this point, and how would it show up on the acceleration vs time plot?

I'd leave out that right hand side vertical line. It's doubtful.

ok i will try this.

 

[physicsnobrain]

So you're saying the acceleration time graph should look like this?

 

[NascentOxygen]

The object instantly goes from having acceleration then goes to 0 acceleration instantly.

Except you told me that we don't know what happens there, where I circled at the right. The recording stops as soon as the object passes through zero displacement. We don't know whether it smoothly continues on to a negative displacement or whether it halts at zero (you drew it showing that it stops at zero, but then clarified that you did that in error). So the end of the graph is an unknown; we definitely cannot say there is a bruising crunch there.

What is happening where I drew the red arrow?

EDIT: Ah, I see you answered already:

Is it when the object moves up, then proceeds to stop moving up instantly?

Yes, there is a sudden change of speed there. So how to improve your acceleration vs time graph to show this happening?

 

[physicsnobrain]

EDIT: Ah, I see you answered already:

Yes, there is a sudden change of speed there. So how to improve your acceleration vs time graph to show this happening?

I'm just not seeing it. When I separate this graph into three distinct segments ( reflective of the three in the displacement time graph) this graph seems to make perfect sense to me:

Also, would a good scenario be similar to the one you said previously, but instead of a t-shirt, a wet toilet paper ball is thrown to the ceiling, sticks to the ceiling for a few seconds, then falls back down?

 

[NascentOxygen]

I'm just not seeing it. When I separate this graph into three distinct segments ( reflective of the three in the displacement time graph) this graph seems to make perfect sense to me:

Okay. Stop right there. Here's an exam question: an object with some initial upward velocity is subjected to the acceleration you show in your graph. Sketch the expected velocity vs time graph.

Also, would a good scenario be similar to the one you said previously, but instead of a t-shirt, a wet toilet paper ball is thrown to the ceiling, sticks to the ceiling for a few seconds, then falls back down?

Yes. I tried various scenarios, including a sticky tennis ball, wet washing, and a spit ball (bogan kids at school would chew up paper and flick a ball of it onto the classroom ceiling!) That dwell time is important.

Now, your graph for the above?

 

[physicsnobrain]

Okay. Stop right there. Here's an exam question: an object with some initial upward velocity is subjected to the acceleration you show in your graph. Sketch the expected velocity vs time graph.

Now, your graph for the above?

The acceleration time graph I made just seems to work for this, I honestly can't figure out the change:

 

[NascentOxygen]

During period A, under the influence of a constant acceleration, the velocity is seen to be steadily decreasing. When acceleration disappears by fading to zero, the velocity will remain as it was at that moment. There is nothing to cause it to suddenly drop to zero speed.

So, can you now sketch expected velocity vs time for the acceleration vs time graph you drew?

 

[haruspex]

The acceleration time graph I made just seems to work for this, I honestly can't figure out the change:

If the velocity changes from a nonzero value to zero in an extremely short time, how great is the acceleration?

 

[physicsnobrain]

If the velocity changes from a nonzero value to zero in an extremely short time, how great is the acceleration?

not very great. Perhaps if I draw it less on my graph?

 

[physicsnobrain]

If the velocity changes from a nonzero value to zero in an extremely short time, how great is the acceleration?

You're saying it should look like this:

 

[NascentOxygen]

No, that is not it.

 

[physicsnobrain]

Ok, well thanks for the help. The assignment is now due.

 

[physicsnobrain]

It's this. That crunch cut it short didn't it.

 

[physicsnobrain]

Also perhaps this could be the scenario. The crunch represents its change from negative acceleration to positive for a brief moment then back to zero.

 

[NascentOxygen]

If the acceleration only lasted a short time, like you have drawn, then at the end of that short time the object would continue on with a steady speed until some acceleration did again act on it.

 

[physicsnobrain]

IS IT THIS?? This I think represents it because it can't instantly go to zero velocity right?

 

[physicsnobrain]

I think this is accurately representing it, i remember you saying something about the vertical line to the right. Its this isn't it?

 

[NascentOxygen]

Also perhaps this could be the scenario. The crunch represents its change from negative acceleration to positive for a brief moment then back to zero.

You are getting the idea. A short sharp force acted to cause the object to lose all of its speed in a very brief moment. But it's not above the axis, that would cause it to rise up faster.

 

[physicsnobrain]

You are getting the idea. A short sharp force acted to cause the object to lose all of its speed in a very brief moment. But it's not above the axis, that would cause it to rise up faster.

So I remove the vertical line like you said before?

 

[NascentOxygen]

This is the graph I refer to. You show the spike of acceleration in the right place, but it should not be above the line, it should be below. You need it to act so it slows the object rapidly to stop it. Like bumping your head on an overhead steel beam! <crunch!>

 

[physicsnobrain]

This is the graph I refer to. You show the spike of acceleration in the right place, but it should not be above the line, it should be below. You need it to act so it slows the object rapidly to stop it. Like bumping your head on an overhead steel beam! <crunch!>

Ahhh, so its slow acting. SO like this:

 

[NascentOxygen]

Ahhh, so its slow acting. SO like this:

When you bump your head on an overhead beam, it doesn't feel like a gentle slow-acting stop to me!

Your graph is improving. Not far to go now ...

 

[physicsnobrain]

Ahhh, it must be this then.

 

[NascentOxygen]

Ahhh, it must be this then.

Not quite, but you are close. It's not as complicated as you show. But you have had enough help with this assignment that I think that should do for now. If you think about it more carefully, you might be able to get 100%. Post again if you come up with a better plot.

Remember that I said that vertical line on the extreme right is questionable, for the acceleration vs time plot, as I explained earlier. I would omit it.