 | Physik M 513.805 (511.015) |
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| Physik M 513.805 (511.015) |
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Force → Acceleration → Velocity → PositionSometimes the position vector is unknown but the force or the acceleration are known as a function of time. It is then possible to integrate the acceleration to find the velocity and integrate the velocity to find the position. $$ \vec{F}\text{ [N]},$$ $$\vec{a}=\frac{\vec{F}}{m}\, [\text{m/s}^2],$$ $$ \vec{v}= \int\limits_{t_0}^{t} \vec{a}(t') dt' + \vec{v}(t_0)\text{ [m/s]},$$ $$ \vec{r}=\int\limits_{t_0}^{t} \vec{v}(t')dt' + \vec{r}(t_0)\text{ [m]}.$$
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