# Simple Physics (unit analysis)

• Afide
In summary, the conversation is discussing equations that involve distance (d), time (t), and speed (v) and determining which ones are incorrect based on unit analysis. The correct equations should have units of distance divided by time (such as m/s for velocity). The discussion also includes a clarification that the standard unit for distance is meters (m).
Afide

## Homework Statement

1. (5 points)
If d is a distance, t is a time, and v is a speed, which of the following equations do unit analysis show must be wrong?

A. d = vt
B. v = 3 d^2 / t
C. t = d/v
D. v = d/t + 2 t/d
E. v = d^2 / t^2

I haven't done this since high school and have no idea. It's pretty easy, but I don't remember this at all. Any help would be greatly appreciated, thanks guys!

Here's an effort of what I think its asking for..

A. d = vt
KM = KM/s(s) KM =/= KM^2 [WRONG]

B. v = 3 d^2 / t
KM/s^2 = 3KM^2 / sec KM/s^2 =/= km^2/s [WRONG]

C. t = d/v
sec = KM / KM/s^2 sec =/= s^2 [WRONG]

D. v = d/t + 2 t/d
KM/s^2 = KM/s + 2s/KM ?

E. v = d^2 / t^2
KM/s^2 = KM^2 / s^2 ?

idk.. >.<

Velocity is in m/s not m/s^2 or km if you want though meters is the standard.

Afide said:
Here's an effort of what I think its asking for..
D. v = d/t + 2 t/d
KM/s^2 = KM/s + 2s/KM ?

E. v = d^2 / t^2
KM/s^2 = KM^2 / s^2 ?

In addition to distance usually being in meters (m) and the unit for velocity being distance/time (m/s) as Chunkysalsa pointed out,

For (D); do those two terms have the same units? If so, you're golden. If not, you have a problem.

For (E) you've done the dimensional analysis correctly, so ask yourself if the right hand side is in units of distance/time.

I would first clarify the units being used for each variable. Distance is typically measured in meters (m), time in seconds (s), and speed in meters per second (m/s). Using this information, I would analyze each equation by checking if the units on both sides of the equation are consistent.

A. d = vt
Units on the left side: meters (m)
Units on the right side: meters per second (m/s)
This equation is consistent and therefore correct.

B. v = 3 d^2 / t
Units on the left side: meters per second (m/s)
Units on the right side: meters squared per second (m^2/s)
This equation is not consistent and therefore must be wrong.

C. t = d/v
Units on the left side: seconds (s)
Units on the right side: meters per second (m/s)
This equation is consistent and therefore correct.

D. v = d/t + 2 t/d
Units on the left side: meters per second (m/s)
Units on the right side: meters per second (m/s) + seconds per meter (s/m)
This equation is not consistent and therefore must be wrong.

E. v = d^2 / t^2
Units on the left side: meters per second (m/s)
Units on the right side: meters squared per second squared (m^2/s^2)
This equation is not consistent and therefore must be wrong.

In conclusion, equations B, D, and E do not pass unit analysis and must be wrong. Equations A and C are consistent and therefore correct.

## 1. What is unit analysis in simple physics?

Unit analysis in simple physics is the process of using units to check and verify the correctness of an equation. It involves checking if the units on both sides of the equation are the same, and if not, converting them to the same units to ensure the equation is balanced.

## 2. Why is unit analysis important in simple physics?

Unit analysis is important in simple physics because it helps to prevent mistakes and errors in calculations. It also ensures that the final answer has the correct units, which is essential for understanding and communicating the results of an experiment or calculation.

## 3. How do you perform unit analysis in simple physics?

To perform unit analysis in simple physics, you must first identify the units for each quantity in the equation. Then, check if the units on both sides of the equation are the same. If they are not, use conversion factors to convert the units to the same base units. Finally, check if the resulting units are correct and match the units of the final answer.

## 4. Can unit analysis be used in all branches of physics?

Yes, unit analysis can be used in all branches of physics. It is a fundamental concept that applies to all equations and calculations, regardless of the specific field of physics. It is a useful tool for double-checking the accuracy of calculations and ensuring that the final results make sense.

## 5. How does unit analysis relate to dimensional analysis?

Unit analysis and dimensional analysis are closely related concepts. Both involve checking the units of an equation to ensure they are balanced and correct. However, dimensional analysis also involves using the fundamental dimensions (length, mass, time, etc.) to derive equations and solve problems, while unit analysis is primarily used for checking the correctness of an equation.

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