Question

HELP!!! Consider the equations

I. v = v0 + ax
II. y = (2m) cos(kx), where k = 2m^-1
III. v^2 = ax

Which ones are dimensionally correct?

Answer 1

I v = v0 + ax
if x=time, correct

II y = (2 m) cos(kx), where k = 2 m−1
y=2cos2x
x=time, incorrect.

III v2 = ax
if x=time, incorrect

Answer 2

That is what I thought at first, but I don't think it's right.

Answer 3

why ? what the problem ?!

Answer 4

In case x isn't = time, suppose x represents a distance.

Answer 5

Ooh ! ya thats right
because if we suppose x represents a distance ,, it`s become : v = v0 + ax
if v is velocity, x is distance and a is acceleration, this is not correct !

Answer 6

So, which ones would be correct? So, I know v = v0 + ax is not correct, but the other two?

Answer 7

I think the second one is correct!

Answer 8

no i don`t think. because if we try like that : the dimension of v is Length/Time while the dimension of (a.x) is L²/T² ..we find that one is not correct !



So ,,maybe the third one is correct :
v² = ax
[v²] = (L / T)² = L² / T²
[ax] =[a][x] = (L / T²) L = L² / T²
therefore [v²] = [ax]
(L and T stand for Length and Time dimensions)

Answer 9

So, just the third one will be correct?

Answer 10

yes .. just the third one

Answer 11

Because the second one is y = (2m) cos(kx), where k = 2m^-1.

Answer 12

Equation II is not correct because [y] = Length (y is a displacement in harmonic oscillation) while both 2π and cos(2π-1)x are dimensionless.

Answer 13

Oh yeah! That's right! So, just Equation III will be the correct one, right?

Answer 14

right :)

Answer 15

Okay, thank you so much! I appreciate it! :-)

Answer 16

Welcome :)