Suppose a predator is pursuing a prey, both individuals are modelled as point particles moving in a Euclidean plane or in Euclidean space. The predator and prey have a respective upper bound $a_P, a_p>0$ on their magnitude of their acceleration. They also have a respective upper bound $v_P, v_p>0$ on their speed. Finally there is of course their initial separation $D>0$. For which values of $(D,v_P,v_p,a_P,a_p)$ is the predator able to catch the prey?
(I forgot to say something about their initial velocity... be free to discuss this if it matters for the outcome. Of course initial speeds exceeding the aforementioned bounds are forbidden.)