Maths problem

E92

Why not do the 3 straight line montion formulas in Physics by integration? no learning, once you understand how to do integration.

JC 2K3

^Because LC Physics doesn't teach integration.

E92

Just cause you're not thought it doesn't mean u can't use it! Thats the way we learned them. I know they dont show it on the marking scheme that way but just like L'Opital's rule for Trig Limits in Maths(which is also not on the Maths Syllabus and we're not supposed to be thought that either) you can use it, and rightly so, its still right(and a lot easier)

JC 2K3

I dunno about easier, linear motion formulas are pretty damn easy to prove anyway.

With so much else you have to assume in LC Physics, I think that for this subject I'll just use the rote learning method of proving things.

MathsManiac

cocoa wrote:

no, derivation still doesn't necessarily show it is true... For example, derive from first principals. It is not necessary to show what first principals are or that they are true, you are allowed to work from assumptions. When proving something, you have to go the extra step.

Not so. Every proof requires assumptions. Even in the most formal of maths logic contexts, (which we weren't talking about anyway,) proofs always involve either axioms or previously established theorems (or both).

Indeed, a proof in such formal contexts is defined as a finite sequence of well-formed expressions, each of which is either an instance of an axiom or follows from earlier expressions in the sequence by a rule of inference of the system. Clearly, no proof can exist without axioms.

Stepping back from this formal context, your example doesn't stand up either, (assuming you're talking about differentiating from first principles). "Derive from first principles" is an example of something that would be equivalent to "prove from first principles". Since "first principles" means that you are operating solely from the very definition of the derivative and not using any other more advanced results, it's as rock-solid a proof as you can get in calculus.

dan719

Eh taught and not 'thought' yeah?

Also newtons second law actually states that f is proportional to the rate of change of momentum, we make it equal by allowing k=1 because of the definition of the newton, so you will certainly lose marks. Go look at the marking scheme.

JC 2K3

^Well that's if you're asked to state Newton's second law.

It's not necessary at all in the derviation of v = u + at.

dan719

I know that, the derivation of v=u+at is merely manipulation of the definition of acceleration. a=(v-u)all over t blah blah blah.

spudington16

obl wrote:

Eh, you can't use the RHS if you have to prove it. Sorta defeats the purpose.

Indeedy... If it says "prove", I'd be inclined to tackle one side (here, the LHS) to arrive at the RHS. Can't recommend multiplying across by the denominator....

Fremen

Indeedy... If it says "prove", I'd be inclined to tackle one side (here, the LHS) to arrive at the RHS. Can't recommend multiplying across by the denominator....

If you multiply across by the denominator, and apply the sum/product formulas, what you get reduces to a true statement. You probably get something like sin5x + sin3x = sin5x + sin3x, though I haven't done it.

Essentially, this gives the proof "in reverse". If you wanted to be really pedantic, you could reverse the order of the steps, starting with a true statement and working up to the equation given in the problem. That would be a correct proof.