Dimensionally corect equation ?

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The discussion centers on the dimensional correctness of the equation X = 1/2 at^3. Participants clarify that in dimensional analysis, scalar coefficients like 1/2 are dimensionless and can be ignored. The equation simplifies to checking if [L] = [L]/[T]^2 * [T]^3 holds true, which it does. Thus, the equation is dimensionally correct. The focus is on understanding that only the dimensions matter in this context.
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Homework Statement



-------------Dimension------------------...
distance (x) (L) Acceleration (a) (L)/(T)^2

Time (t)-----> (T) Force (F)-----> (M)(L)/(T)^2

Mass (m)----> (M) Energy (E)-----> (M)(L)^2/(T)^2

Speed (v)-----> (L)/(T)
Is the following equation dimensionally correct?
A) X= 1/2 at^3

Homework Equations





The Attempt at a Solution



A) X= 1/2 at^3
[L] = 1/2 [L]/[T]^2 * [T]^3

i know my proff said numbers such as 1/2 don't have dimension but i don't really understand how to solve this...what am i suppsoed 2 do with 1/2
 
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Welcome to PF Star20,

QUOTE=star20;1867892]

A) X= 1/2 at^3
[L] = 1/2 [L]/[T]^2 * [T]^3

i know my proff said numbers such as 1/2 don't have dimension but i don't really understand how to solve this...what am i suppsoed 2 do with 1/2[/QUOTE]
Scalar coefficients are irrelevant in dimensional analysis, only the dimensions themselves are important, you can safely ignore the fact of 1/2.
 
Drop the (1/2). It doesn't have any dimensions.
 
ok thanks
 

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