# Answer to Question #2797 in Mechanics | Relativity for muskan

Question #2797

Prove graphically and anatically following equations of motions;

1.) v = u+at

2.)v

3.)s = ut+1/2at

1.) v = u+at

2.)v

^{2}= u^{2}+2as3.)s = ut+1/2at

^{2}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

∫v

where x

If body has nonzero acceleration than

at

where a is the acceleration.

If x

at

Differentiating this expression we get

x' (t) = v

And that is formula 1.

v = v

S = v

t = (v-v

S=v

a=(v

v

This is formula 2.

This graph illustrate function

v

This graph illustrates function

at

Area under the line for given interval of t gives S.

∫v

_{0}dt = v_{0}t + x_{0}= x(t)where x

_{0}is the initial position.If body has nonzero acceleration than

at

^{2}/2+v_{0}t+x_{0}=x(t)where a is the acceleration.

If x

_{0}=0 we get formula 3.at

^{2}/2 + v_{0}t = x(t) - x_{0}= x(t) = S.Differentiating this expression we get

x' (t) = v

_{0}+at = v(t)And that is formula 1.

v = v

_{0}+atS = v

_{0}t+(at^{2})/2t = (v-v

_{0})/aS=v

_{0}(v-v_{0})/a+(a(v^{2}-2v^{2}v_{0}^{2}+ v_{0}^{2}))/(2a^{2}) = (v^{2}-v_{0}^{2})/2aa=(v

^{2}-v_{0}^{2})/2Sv

^{2}=v_{0}^{2}+2Sa.This is formula 2.

This graph illustrate function

v

_{0}t+x_{0}=x(t).This graph illustrates function

at

^{2}/2 + v_{0}t + x_{0}= x(t)Area under the line for given interval of t gives S.

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## Comments

Assignment Expert08.08.11, 13:20You are welcome!

Ayush07.08.11, 12:05I think that your information was much of help to me.

Thankx.

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