PHYSICS:disGRAPH:1D MOTION (displacement,time,velocity involved)

[blissful kayak]

please dont use difficult terms , use ez language keeping the scientist aside,

part 1: for the first half of the time the displacement is increasing constantly
Δs=y2-y1

personal question:

1. how do the different velocities affect the:
   -topmost height reached by the 2 objects(does the low velocity object reach height lower than the high velocity obj)
2. if the objects met in the air before reaching the ground
   then displacement wud have been 0 somewhere in the mid of the graph , how does it look? n work

part 2: for the sec half of the time the displacement between the objects is decreasing , but not linearly, why is it 4th?

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[slender granite]

@blissful kayak what did you try?

What do you think is same in both stones?

[blissful kayak]

the gravity acting on them when they come back on the ground

[polar narwhal]

Yeah, that's right

Not just back on the ground though, it's through the entire process

If you remember, we have that $y=y_0+v_{y_0}t+a_yt^2$, where $y$ is the position, $y_0$ is the initial position (assume it is 0), $v_{y_0}$ is your initial velocity, and $a_y$ is the acceleration in the $y$-direction

[valid orchid]

Kocher

[polar narwhal]

This will be a parabolic arch; the velocities change the time where the objects peak and the position where they peak as well

To answer the 2nd question, yes, displacement would be 0 if they are at the same position at the same time. However, since the accelerations are the same, they will not intersect, given that the initial velocities are different (try to prove this algebraically by settings the equations equal).

[slender granite]

@blissful kayak try to visualize one thing for me if you sit on one of the stones and look at the other how would you see the other going?

[blissful kayak]

if i choose to sit on the slower stone, and my stone tossed after the faster one, ill see separation between us is increasing as the time passes and and later, the separation btween us is decreasing as the faster stone reaches the maximum height point, and comes down under the influence of gravity, the separation btween us is decreasing. (if my slower stone is tossed before the faster one, for a very short period of time , the displacement between us will decrease, then after a very small distance the faster stone will have same distance and time as my stone, and after that the distance btween us/ between both stones will increase, then again after the max height separation will decrease/distance btween us decreases. and its zero when both reach ground(which does not happen at the same time? no?)

[slender granite]

OK so when you are sitting on that rock you are accelerating down right?

And so is the other rock

So from your frame the acceleration of the other stone SHOULD BE ZERO

Can you visualize that?

@blissful kayak

[blissful kayak]

yes , cuz we're having the same acceleration so the other stone will appear to be at rest for me, until i hit the ground

[blissful kayak]

i like the visualisation thing...

what to do next

and how do i do it mathematically, i find it hard

[slender granite]

You are almost right but you will not see the other stone at rest because initially velocities were different you would see it move with a CONSTANT velocity

After you hit the ground it will appear to accelerate again

With this much info we can clearly see which graph is correct

If you didn't have options
You can do further steps After visualization mathematically to get the exact graph

[bold tide]

@blissful kayak

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[slender granite]

@blissful kayak so you see first constant then Downward parabola so option (D)

[blissful kayak]

okaay, thankyou so much, sir, i understood it.

[slender granite]

You can +close if it's all clear

[blissful kayak]

+close

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