# 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[sup]2[/sup] = u[sup]2[/sup]+2as
3.)s = ut+1/2at[sup]2[/sup]
1
2011-06-15T11:44:44-0400
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
&int;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.

This graph illustrate function
v0t+x0=x(t).

This graph illustrates function
at2/2 + v0t + x0 = x(t)
Area under the line for given interval of t gives S.

Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

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.