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Answer to Question #2797 in Mechanics | Relativity for muskan

Question #2797
Prove graphically and anatically following equations of motions;
1.) v = u+at
2.)v2 = u2+2as
3.)s = ut+1/2at2
Expert's answer
Let x(t) be the position of some body. Let v(t) be the velocity of some body. Than its position at any moment of the time will be
∫v0 dt = v0 t + x0 = x(t)
where x0 is the initial position.
If body has nonzero acceleration than
at2/2+v0 t+x0=x(t)
where a is the acceleration.
If x0=0 we get formula 3.
at2/2 + v0 t = x(t) - x0 = x(t) = S.
Differentiating this expression we get
x' (t) = v0+at = v(t)
And that is formula 1.
v = v0+at
S = v0 t+(at2)/2
t = (v-v0)/a
S=v0 (v-v0)/a+(a(v2-2v2 v02 + v02))/(2a2 ) = (v2-v02)/2a

a=(v2-v02)/2S
v2=v02+2Sa.

This is formula 2.
../../..//assignments/uploaded_files/static/5c/38/5c38c0d3d87d92ce74c8123fb020e025.png
This graph illustrate function
v0t+x0=x(t).
../../..//assignments/uploaded_files/static/79/76/797660f41db692bb125aa2475cd6d42d.png
This graph illustrates function
at2/2 + v0t + x0 = x(t)
Area under the line for given interval of t gives S.

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Comments

Assignment Expert
08.08.11, 13:20

You are welcome!

Ayush
07.08.11, 12:05

I think that your information was much of help to me.
Thankx.

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