homogeneous equation..

what is one ? :confused:

my teacher has never told me :confused:

and how do i show that s=u x t + (1/2) x a x t(squared) is homogeneous

i know this is an equation of motion but how is homogeneous? help! thanks

Reply 1

Ribbons

schizophrenic

what is one ? :confused:

my teacher has never told me :confused:

and how do i show that s=u x t + (1/2) x a x t(squared) is homogeneous

i know this is an equation of motion but how is homogeneous? help! thanks

a homogenous equation is one in which the base units on either sides are equal...itll be clearer if we look at the equation u mentioned:

s=ut+1/2at²
s is measured in metres, so on the left hand side (lhs), u have m,
RHS:
u have a which is measured in m/s² . and time t is measured in s, u is measured as m/s and t is s....
so u have
s=ut+1/2 a t²
m=m/s x s +ms^-2 (s)²

the secs go (s² cancels the s^-2etc)

and so u have

m=m (since m+m=m)

since the base units on both the sides are equal, the equation is homogenous

Reply 2

AlphaNumeric

^ Since the equation in question is a physical one, the units MUST match or else the equation doesn't make any sense, you'd end up showing 10 metres was equal to 5 second, or 20 Joules is equal to 5 Newtons, thats logically and physically inconsistent.

The term "homogeneous" typically corresponds to linear differential equations. They are homogeneous if there is no term which doesn't involve a derivative of y (including the zeroth derivative). http://mathworld.wolfram.com/HomogenousOrdinaryDifferentialEquation.html

I've never heard it related to an equation like s = ...., obviously the term has a different meaning I've not come across.

Reply 3

Ribbons

AlphaNumeric

The term "homogeneous" typically corresponds to linear differential equations. They are homogeneous if there is no term which doesn't involve a derivative of y (including the zeroth derivative). http://mathworld.wolfram.com/HomogenousOrdinaryDifferentialEquation.html

I've never heard it related to an equation like s = ...., obviously the term has a different meaning I've not come across.

that looks like a more mathematical approach(much more advanced than A level maths for sure). I might be wrong......but in physics, the term homogenous equation is related to all the equations like s=...etc etc.....and is used to work out whether the given eqaution is correct by simply finding the units on either side of the equation.