Consider two particles $\backslash ($ P $\backslash )$ and $\backslash ($ Q $\backslash ),$ such that they have the same mass $\backslash ($ m $\backslash ),$ and are connected by a tether of length $\backslash (2$ l $\backslash ).$

Each particle is subject to a force that is perpendicular to the direction of the tether as shown below.

The force is equal in magnitude, $\backslash ($ F $\backslash ),$ for both particles. Assume there is NO gravity acting on the system, also assume the system starts with zero initial velocity.

Determine the time duration, $\backslash ($ t $\backslash ),$ for which a force $\backslash ($ F $\backslash )$ can be applied such that none of the particles will exceed a chosen specific net acceleration of value $\backslash ($ a$\_\{\backslash$text $\{$Max $\}\}\backslash ).$ Your answer will be a function of $\backslash ($ a$\_\{\backslash$text $\{$Max $\}\}\backslash ).$