Suppose that a student guesses (incorrectly) that the displacement (x), velocity (v), and acceleration (a) are related by the following equation: v^2 = ax. Check the dimensions of each side of the relationship to see if they are the same.
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So, dimensions are like, what you are measuring. There is distance, which would usually be in meters, kilometers, etc. There is time, often measured in seconds, minutes, hours... And velocity, in m/s, km/h, etc.... And acceleration, in m/s^2, km/h^2, etc...
But the dimensions are like time, velocity, acceleration.
You have some variables that are commonly used for certain dimensions.
That incorrect thought was that \(v^2=a\ x\).
We can check everything by putting in some standard units! For all time, we'll use seconds, and for distance, meters.
\(x\) is in meters
\(v\) is in meters per second
\(a\) is in meters per second per second.
Do units match? Simplify, and you'll find out!
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