| Velocity | \(\mathbf{v}(t)=\mathbf{r}^{\prime} (t)=\dfrac{dx}{dt} \mathbf{i}+\dfrac{dy}{dt}\mathbf{j}+\dfrac{dz}{dt}\mathbf{k}\) |
| Acceleration | \(\mathbf{a}(t)=\mathbf{r}^{\prime \prime} (t)= \dfrac{d^{2}x}{dt^{2}}\mathbf{i}+\dfrac{d^{2}y}{dt^{2}}\mathbf{j}+\dfrac{ d^{2}z}{dt^{2}}\mathbf{k}\) |
| Speed | \(v(t)=\;\left\Vert \mathbf{v}(t)\right\Vert\;=\;\left\Vert \mathbf{r}^{\prime} (t)\right\Vert\;=\;\sqrt{\left( \dfrac{dx}{dt}\right) ^{2}+\left( \dfrac{dy}{dt}\right) ^{2}+\left( \dfrac{dz}{dt}\right) ^{2}}\) |