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.

Question

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.

theeric · Answer

Hi!

theeric · Answer

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...

theeric · Answer

But the dimensions are like time, velocity, acceleration.

You have some variables that are commonly used for certain dimensions.

$v$  velocity
$x$  distance
$a$  acceleration

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.
So
$x$  is in meters
$v$  is in meters per second
$a$  is in meters per second per second.

Substitution time!
$(m/s)^2=m/s^2\times m$
Do units match? Simplify, and you'll find out!

goformit100 · Answer

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