# B Can I use three equations for the same concept?

#### Indranil

1. v = u + at
2. x = ut + 1/2 at^2
3. u^2 = + 2ax
Can I use three equeations above for the same concept 'constant accelaration' interchangeablly?

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#### PeterDonis

Mentor
Can I use three equeations above for the same concept 'constant accelaration' interchangeablly?
What do you think? What conditions would have to be true for you to be able to use these three equations interchangeably?

#### Doc Al

Mentor
3. u^2 = + 2ax
I would rewrite this one as v^2 = u^2 + 2ax, since you're using u as the initial velocity.

Can I use three equeations above for the same concept 'constant accelaration' interchangeablly?
Those equations are valid for constant acceleration, but do they say the same thing? Hint: Note that each equation relates a different pair of "unknowns".

#### Indranil

What do you think? What conditions would have to be true for you to be able to use these three equations interchangeably?
If a = 0, we get 'velocity' in every equations.

#### PeterDonis

Mentor
If a = 0, we get 'velocity' in every equations.
But what about if $a \neq 0$?

#### Indranil

But what about if $a \neq 0$?
I think, I don't get 'velocity' in every eqeations.

#### PeterDonis

Mentor
I think, I don't get 'velocity' in every eqeations.
I'm not sure what you mean by "get velocity". Only the first equation is an equation for the velocity $v$.

Perhaps we should take a step back and ask: why would you want to use these three equations interchangeably?

#### Indranil

I'm not sure what you mean by "get velocity". Only the first equation is an equation for the velocity $v$.

Perhaps we should take a step back and ask: why would you want to use these three equations interchangeably?
To get the velocity either initial or final velocity. It is my own presumption. I may be wrong with this concept.

#### PeterDonis

Mentor
To get the velocity either initial or final velocity.
The initial velocity is just $u$; you don't solve for that, it's something that should be given in the statement of the problem.

The final velocity $v$ has to be obtained from the first equation. You can't obtain it from the second equation since it doesn't appear at all. The third equation has $v$ in it (at least, it does with the correction @Doc Al gave) but it also has $x$ in it, which is another unknown; so it won't give you $v$ in terms of quantities that are known from the statement of the problem.

#### Doc Al

Mentor
Each of your three equations relates a different pair of unknowns. (As @PeterDonis stated, u is a given, as is the acceleration.)

The first equation relates v & t.
The second equation relates x & t.
The third equation relates v & x.

So each equation describes constant acceleration motion in a different way. Depending upon the particular problem you're dealing with--and the information given--one equation might be more useful than another. While all three deal with accelerated motion, they are not the same.

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