I am currently using the equation:
$$ \vec p=\frac12\vec at^2+\vec vt+\vec x$$ to find the acceleration I need to move from one point to another.
- $\vec p$ = target position (point 2d)
- $\vec a$ = acceleration (vector 2d)
- $t$ = time (scalar)
- $\vec v$ = initial velocity (vector 2d)
- $\vec x$ = initial displacement (point 2d)
I am able to rearrange this equation to find the required acceleration to reach the target in time $t$. But I need to limit the acceleration applied, and the time is irrelevant (it can be any value) to my problem.
Can I rearrange this to find $t$ and $\vec a$ where $\left|\vec a\right |$ is equal to some value $n$?