# Dimensional Analysis Equation Help

• Manda*n
In summary, the question asks which of the given equations are dimensionally correct. The first equation, v^2=v^2+2at, is incorrect because the last term is not squared like the others. The second equation, v^2=v^2+2ax, is correct because all terms have the same dimensions.
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.

(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.

So Simple! Thank you so much.

## 1. What is dimensional analysis?

Dimensional analysis is a mathematical technique used to convert between different units of measurement. It involves setting up and solving equations based on the relationship between different units, in order to convert from one unit to another.

## 2. Why is dimensional analysis important in science?

Dimensional analysis is important in science because it allows for accurate and precise measurements and conversions between different units. It is especially useful when dealing with complex equations or when working with different systems of measurement.

## 3. How do I set up a dimensional analysis equation?

To set up a dimensional analysis equation, you first need to identify the given unit and the desired unit. Then, you need to find the conversion factor between the two units. Finally, you can set up an equation using the given value and the conversion factor to solve for the desired unit.

## 4. Can dimensional analysis be used for any type of unit conversion?

Yes, dimensional analysis can be used for any type of unit conversion as long as the units being converted are related through a conversion factor. This can include conversions between metric and imperial units, as well as between different systems of measurement.

## 5. What are some common mistakes to avoid when using dimensional analysis?

Some common mistakes to avoid when using dimensional analysis include using the wrong conversion factor, using incorrect units, and not canceling out units correctly. It is important to double check all conversions and equations to ensure accuracy.

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