How do u derive the displacement formula? (1 Viewer)

ahohen_77

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Can anyone show me how to derive the displacemment formula:
S=ut+1/2at^2 ?
 

hatty

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the derivative of ut = u (because u is a constant)
the derivative of 1/2at^2 = at
( the power 2 is taken down and is multiplied by the 1/2, hence the 2's cancel out, making it just 1, at remains, and you minus 1 fromt the power 2, hence you are only left with at)

:.
the velocity = u + at.

Q.E.D

how good am i?
i dont even do physics
 
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ahohen_77

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differentiation? i get that...but how does it result in the displacement formula?...my teacher involved the formulas
average velocity=s/t and also average velocity= v+u/2...
 

abdooooo!!!

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well, can't you just visualize this in your head... its pretty simple.

if you want to derive it algebraicly here:

r = vt [since average v = r/t]
= t * (u + v)/2 [since average v = (u + v)/2]
= (ut + vt)/2
= ut + 1/2(vt - ut)
= ut + 1/2(at^2) [since a = (v - u)/t]

:)
 

abdooooo!!!

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just think in your head that the average acceleration will be half the difference between its original velocity and final velocity reached. if you can understand that they the formula should be self explanatory.
 

Heinz

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This is where ext 1 maths come in handy.
S = ut + at is the same as x = vtcos@(vcos@= u, acceleration in the x direction = 0) and y = vtsin@(vsin@= u) - gt( -g = a). Pick up an ext 1 maths text and read the proofs, theyre all derived through integration.
 

abdooooo!!!

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what did you not get in the first place... i don't get that... its so simple lol :p
Originally posted by freaking_out
prolly copied it from a textbook. :D :p
of course he/she did... i mean its not like you just make up such a thing called differential calculus in your head while the human race took thousands of years to develop the theory through knowledge over generation with books. :)
 

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