# Newton's Law¶

## Newton's First Law (Inertia)¶

An object at rest will stay at rest, and an object in motion will stay in motion unless acted on by a net force.

Mathematically, this is equivalent to saying that if the net force on an object is zero, then the velocity of the object is constant.

$$\vec{F} = m\frac{d\vec{v}}{dt} = 0 \quad \rightarrow \quad \vec{v} = \text{constant.}$$

## Newton's Seond Law¶

The rate of change of momentum of a body over time is directly proportional to the force applied, and occurs in the same direction as the applied force.

$$\vec{F} = m\vec{a}$$
• GRE Physics GR1777: Problem 001