# Question #b331e

Oct 3, 2015

The three of laws of Newton are independent, that is why they are called three laws, not just one. But you can use F=ma to "guess" the first law.

#### Explanation:

The first law of Newton states that a body either tends to stay in rest or in a straight line with constant speed; that is, no force is present herein.

If you are familiar with Calculus, you can play a little bit.

$F = m \cdot a$

If we have no force present, which is the case for the first law:

$m \cdot a = 0$

By recollecting the definition of acceleration:

$\ddot{x} \cdot m = 0$

By integrating both sides with respect time:

$\dot{x} \cdot m = k$

k is an arbitrary constant. Recollect that $v \left(t\right) = \dot{x} \left(t\right)$

$v \left(t\right) = \frac{k}{m}$

Which means that the speed is constant, you are either is in rest or constant speed.

If you integrate once more:

$x \left(t\right) = \left(\frac{k}{m}\right) t$

Which means that the higher is the mass, the more difficult it is to move, the inertia, which is the first law of Newton in other terms.