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Maths and Physics (Problems)


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AuthorMaths and Physics (Problems)
my bad.. i thought that was in mains paper..x_X

it's from a DPP
So after a long time..here's a question, maybe just for fun haha..post the answer but not yet the solution please, let everyone try ;)

Q. A particle moves along the positive x-axis, starting form origin (t=0, x=0, velocity = 0). Its acceleration is given by A = 2x^3, where 'x' is it's distance from origin at any point. Find the distance covered by it in 10 seconds.
10km maybe?
Crazy it may seem

but i think 0 (or negligible)
but i think 0 (or negligible)

Give method..I think you are getting a 1/infinity or something after integration? Or what is your approach? :)

Gaara has already got it right, just saying :)
Initial velocity =0
Accn = 0^3=0

So, stationary :3

Anyhow, assuming it made it ahead, you get 1/x on integration.
Hence, tends to 0.
Vdv/dx= 2x³ so v= -x²

Now dx/dt=-x²
So 1/x =t + C
Here c would tend to infinity so at every t, x would tend to 0 (something went wrong,I have an intuition)
hmpf

v dv/dx=2x^3 so v=-x^2

now dx/dt=-x^2

so 1/x=t + C

Here c would tend to infinity so at every t, x would tend to 0 (something went wrong,I have an intuition)


for The One Ring:
on origin,the particle is at an unstable equilibrium,so a slight push (a slight movement) would trigger locomotion (however negligible)

for example if acceleration changed with distance as a=x..a slight movement would trigger an exponential escalation in displacement.
I tried and it gave me -20m lol

I am not cut out for this stuff!! :(
I did this.

2.2x^3.x = (dx/dt)^2

(-+)2x^2 = dx/dt

(-+)2t = -1/x + C

Now we need something to calculate C. :$
its at infinite displacement from the origin just as there guys stated
so a slight push
I don't see that anywhere hmmh
Initial velocity =0
Accn = 0^3=0

So, stationary :3

Anyhow, assuming it made it ahead, you get 1/x on integration.
Hence, tends to 0.


Yea, that's right.


on origin,the particle is at an unstable equilibrium,so a slight push (a slight movement) would trigger locomotion (however negligible)

for example if acceleration changed with distance as a=x..a slight movement would trigger an exponential escalation in displacement.


Where did you assume that "push from"? Besides, what would you define the push to be? Maybe you have a point, I wouldn't be sure of that.
oh

well i've been taught to assume *a slight push* when these type of question occur mainly by seeing "A particle moves along the positive x-axis" so that the question becomes a "solving" type rather than quickies.

Besides what difference does it make??..even when u put t=infinite in 1/x=t + C the particle is still at rest at (x =0)



Besides, what would you define the push to be
no definition..it's just a simple phrase for causing a slight displacement for further movement
Besides, what would you define the push to be
no definition..it's just a simple phrase for causing a slight displacement for further movement


Yes I mean what would you say, is it a momentary velociy or momentary acc etc.
u're taking this too srsly :p

what i meant was the particle got moved to 0.00000000000(and many more 0's)1 somehow from 0 (Just an assumption that the particle made it ahead by some means..still at the end proving it never moved)
Stop.
Stop.
Pun intended.
xD
integrate root over tan x :p
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