Definition:Component of Vector/Examples
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Examples of Components of Vectors
Acceleration
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:
- $\mathbf a = \dfrac {\d^2 x} {\d t^2} \mathbf i + \dfrac {\d^2 y} {\d t^2} \mathbf j + \dfrac {\d^2 z} {\d t^2} \mathbf k$
where:
- $\mathbf r = x \mathbf i + y \mathbf j + z \mathbf k$