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~~Find position of a particle at a time~~

How to find position of a particle at a time given a position dependent force

If we have a force which changes depending on the position of a particle, how can we find the position of the particle at some time $t$?
We can find its velocity if it has travelled a given distance
$$ \int^{r_f}_{r_o} F(r)dr = \frac{1}{2} \cdot m_p(u_f^2 - u_o^2) $$
~~but this equation doesn't involve time and I don't see how we can 'generate' time from a position varying force. Any help?~~

If we have a force which changes depending on the position of a particle, how can we find the position of the particle at some time $t$?
We can find its velocity if it has travelled a given distance
$$ \int^{r_f}_{r_o} F(r)dr = \frac{1}{2} \cdot m_p(u_f^2 - u_o^2) $$
but this equation doesn't involve time and I don't see how we can 'generate' time from a position varying force.

time newtonian-mechanics forces

time newtonian-mechanics forces