# Why did Newton state his first law separately even though it is apparently a direct consequence of the second law? [duplicate]

If $F=0$, $F=ma \implies m\frac{(v-u)}{t}=0\implies v-u=0 \implies v=u$

Which is essentially Newton's first law.

## marked as duplicate by ACuriousMind♦, Community♦Jun 3 '16 at 13:56

But here is an additional side-note to be considered:

$$a= \frac{v-u}{t}\;;$$

Hmm; this is not true in general.

What you would want to say is that

$$F~=~ m\frac{\mathrm dv}{\mathrm dt} = ma~=~0$$

However, that doesn't mean that the body has constant velocity; for in some cases

$$\dot a ~\ne~ 0\;.$$