# Are these three formulas correct?

## If Force = $F$ , Acceleration = $a$ , and Mass = $m$ does that mean Force = $m$$\times$$a$ Acceleration = $\frac{F}{m}$ Mass = $\frac{F}{a}$ or did I include a mistake in my work?

Apr 4, 2016

These are all correct!

#### Explanation:

100% right
$F = m a$
so $a = \frac{F}{m}$ and $m = \frac{F}{a}$

Apr 5, 2016

Correct mathematical representation of the last formula is
$m = | \vec{F} \frac{|}{|} \vec{a} |$

#### Explanation:

Especially the last formula assumes that while trying to obtain the value of mass $m$, a scalar quantity, by dividing two vector quantities; Force $\vec{F}$ by acceleration $\vec{a}$ the division is performed between two scalars, i.e. , the magnitudes of two vectors involved.
It is a convention and is understood.

Needless to say that the acceleration is produced by the force and therefore, these two vector quantities have the same direction. Strictly, speaking the correct formula should look like
$m = | \vec{F} \frac{|}{|} \vec{a} |$,

Similarly, to be precise one may also write the remaining two expressions as

Force $\vec{F} = m . \vec{a}$ and
Acceleration $\vec{a} = \frac{1}{m} \vec{F}$