I think I'm making a mistake to reach my goal.
I would like to find an $x[t]$ function that could describe the following conditions:
1 - The object is in position $x=151$ (meters) at time $t=5$ (second).
2 - The object is in position $x=1215$ (meters) at time $t=59$ (second).
3 - The object has velocity $v=0$ (meters/second) at time $t=5$ (second).
4 - The object has velocity $v=0$ (meters/second) at time $t=59$ (second).
5 - The object has acceleration $a=1$ (meters/second^2) at time $t=5$ (second).
6 - The object has acceleration $a=0$ (meters/second^2) at time $t=59$ (second).
DSolve[{x[5] == 151, x[59] == 1215, x'[5] == 0, x'[59] == 0,
x''[5] == 1, x''[59] == 0}, x[t], t]
The goal
The idea is that the object be stopped at position $x=151$, be accelerated and decelerate at a certain point in the path (which may actually be random), so that when it reaches position $x=1215$, it stops.
{5, 59}
. Choose coefficients such that the six boundary conditions are satisfied. $\endgroup$ – bbgodfrey Dec 27 '17 at 14:47