Motion of Body with Constant Mass

From ProofWiki
Jump to navigation Jump to search


Let $B$ be a body with constant mass $m$ undergoing a force $\mathbf F$.

Then the equation of motion of $B$ is given by:

$\mathbf F = m \mathbf a$

where $\mathbf a$ is the acceleration of $B$.


\(\ds \mathbf F\) \(=\) \(\ds \map {\dfrac \d {\d t} } {m \mathbf v}\) Newton's Second Law of Motion
\(\ds \) \(=\) \(\ds m \dfrac {\d \mathbf v} {\d t} + \mathbf v \dfrac {\d m} {\d t}\)
\(\ds \) \(=\) \(\ds m \dfrac {\d \mathbf v} {\d t} + 0\) Derivative of Constant
\(\ds \) \(=\) \(\ds m \mathbf a\) Definition of Acceleration