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Physics Equasion (Proof)?

So, my teacher told us that we were going to write a test on these 2 equations:

1.

u = u0 + αt

2.

s = u0t+1/2at2

I don't have problem on the first equation as it's pretty simple:

u = u0 + αt <=>
(u-u0)/α = (a * t)/a <=>
t = (u-u0)/a

But when it comes to the second equation, it is so long and hard to remember.

So, has anyone got a quick and easy way to prove the equasion s = u0t+1/2at2 ?

Thanks in advance!
(edited 8 years ago)
Draw a velocity-time graph of a moving body with constant acceleration. The area under the graph is the displacement 's'. The gradient of the graph is constant between u0 and u. Can you work it out from there?
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Avatar for Coto
Coto
OP
Original post by MathsAstronomy12
Draw a velocity-time graph of a moving body with constant acceleration. The area under the graph is the displacement 's'. The gradient of the graph is constant between u0 and u. Can you work it out from there?


Nope, graphs/diagrams are not the case here... He has written the equation like the first equation, until he gets to:

u2-u02 = 2as <=>
u2=u02+2as <=>
u = [sqrt]u02 + 2as[/sqrt]

So I bascailly want it to end to that without any diagrams/graphs, just text proof.
are u finding it to derive the equation or rearranging it? What u said in the 1st post is rearranging the eqaution v-u/t=a. Proof is deriving it and what the other guy said is how u derive the equation
(edited 8 years ago)
Sorry for the lack of LaTex but

S = (u+v)/2 *t
This should make intuitive sense Displacement = average speed * time

but v = u +at
Sub in u+at for v and you get
S=(u+u+at)/2 * t
S = (2u+at)/2 *t
S = ut +1/2at^2

To be honest you should probably just learn the equation but knowing the proof cant hurt.
Original post by Coto
Nope, graphs/diagrams are not the case here... He has written the equation like the first equation, until he gets to:

u2-u02 = 2as <=>
u2=u02+2as <=>
u = [sqrt]u[/sqrt]02 + 2as

So I bascailly want it to end to that without any diagrams/graphs, just text proof.


Okay.. don't really understand your question but I'll try and help; I thought you were asking for the proof of s=ut+1/2at^2 which can be shown graphically by calculating areas. Proving v^2=u^2 +2as is simple. You know that v=u+at (def of accelleration) so square both sides becomes v^2 = u^2 +2uat +a^2t^2. Then subbing in s=ut+1/2at^2 gives v^2=u^2+2as.
Reply 6
Avatar for Coto
Coto
OP
Original post by MathsAstronomy12
Okay.. don't really understand your question but I'll try and help; I thought you were asking for the proof of s=ut+1/2at^2 which can be shown graphically by calculating areas. Proving v^2=u^2 +2as is simple. You know that v=u+at (def of accelleration) so square both sides becomes v^2 = u^2 +2uat +a^2t^2. Then subbing in s=ut+1/2at^2 gives v^2=u^2+2as.


Yes, that's what I want, but I want to prove the s=ut+1/2at2 equation by the beginning, not by the point where it gets to v2=u2+2as.

Just imagine the question was: "Prove" the equation: x = u*t+1/2a*t2

What would I write?
Original post by Coto
Yes, that's what I want, but I want to prove the s=ut+1/2at2 equation by the beginning, not by the point where it gets to v2=u2+2as.

Just imagine the question was: "Prove" the equation: x = u*t+1/2a*t2

What would I write?


Honestly I think the best way is by showing it graphically but there is an algebraic method too. You know the average velocity = (u+v)/2 and that v=u+at. therefore average velocity= (2u+at)/2. Average velocity x time duration = displacement therefore (2u +at)/2 x t = ut+1/2at^2

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