Dimensional Analysis Equation Help

[Manda*n]

Homework Statement

The question states which of the following equations are dimensionally correct?
(a) v^2=v^2+2at or (b) v^2=v^2+2ax

Homework Equations

v=[L]/[T], x=[L], a=[L]/[T]^2

The Attempt at a Solution

(a) v^2=v^2+2at
[L]^2/[T]^2=[L]^2/[T]^2+([L]/[T]^2)([T])
[L]^2/[T]^2=[L]^2/[T]^2 + [L]/[T]

(b)v^2=v^2+2ax
[L]^2/[T]^2=[L]^2/[T]^2+([L]/[T]^2)([L])

The correct answer listed is b.. I just don't understand why a is incorrect while b is correct.
Can someone please explain? Thanks!

 

[chrisk]

(a) v²=v²+2at
[L]²/[T]²=[L]²/[T]² + [L]/[T]

The last term [L]/[T] is not squared like the other two.

(b)v²=v²+2ax

[L]²/[T]²=[L]²/[T]²+([L]/[T]²)([L])

The last term

([L]/[T]²)([L])=([L]²/[T]²)

and this is of the same dimensions as the other two terms.

 

[Manda*n]

So Simple! Thank you so much.