Simple Physics (unit analysis)

[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!

 

[Afide]

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.. >.<

 

[Chunkysalsa]

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

 

[fss]

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.

 

[rwisz]

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.