Optimize For minimum Acceleration

I have body with initial velocity u = 40/3 meter per second, and initial position x = 0 meter. Now, I need to find the minimum value of acceleration (a) such that body stops before 0.45 meter (i.e. s<= 0.45). The governing equations will be kinematics equation (They are basically ode). Acceleration may be assumed as function of time or constant till the body stops (any solution will work for me).

s = u*t + 0.5*a*(t^2);

v = u + a*t;

here v is velocity at any time "t" and s is position at any time "t" (t<=0.2 sec or 200 milliseconds).

It will be really helpful if someone can guide me to solve it, provide a solved example or if possible provide a with solution.

Answer 1

[Torsten]

For constant acceleration, the equations to determine a and tstop are

x'(tstop) = 40/3+a*tstop = 0
x (tstop) = 40/3*tstop+0.5*a*tstop^2 = 0.45

Best wishes

Torsten.