Definition:Component of Vector/Examples/Acceleration

Example of Components of Vector
Let $\mathbf a$ be an acceleration of a particle $P$ in space.

Then we have:
 * $\mathbf a = \dfrac {\d \mathbf v} {\d t} = \dfrac {\d^2 \mathbf r} {\d t^2}$

where:
 * $\mathbf v$ is the velocity of $P$ at time $t$
 * $\mathbf r$ is the displacement of $P$ at time $t$.

Thus:
 * $\mathbf a = \dfrac {\d^2 x} {\d t^2} \mathbf i + \dfrac {\d^2 x} {\d t^2} \mathbf j + \dfrac {\d^2 x} {\d t^2} \mathbf k$

where:
 * $\mathbf r = x \mathbf i + y \mathbf j + z \mathbf k$