PX285 - A1 - newton's laws

first law

a body stays in a state of constant motion unless acted upon by an external force

\vec{v} = c o n s t a n t (\vec{F} = 0)

second law

force is rate of change of momentum

\vec{F} = m \vec{a}

third law

to every action, there is an equal and opposite reaction

\sum_{i} {\vec{F}}_{i} = 0

for a mass, $m$ , with $\vec{g} \sim - \hat{z}$ , the force is: $- m g \hat{z} = m \ddot{\vec{z}}$

\begin{aligned} - m g & = m \ddot{z} \\ \int \ddot{z} d t & = \int - g d t \\ \dot{z} & = - g t + v_{0} \\ \int \dot{z} d t & = \int (- g t + v_{0}) d t \\ z (t) & = - \frac{1}{2} g t + v_{0} t + z_{0} \end{aligned}