An ion source in a mass spectrometer produces a beam of ions of mass MMM and charge QQQ. These ions are accelerated from rest through an electrostatic drift chamber across a potential difference UUU, emerging with a terminal speed uuu.
A second species of ion, having a mass of M2\frac{M}{2}2M and a charge of 5Q5Q5Q, is accelerated from rest through a potential difference of 3U3U3U in the same apparatus.
Determine the terminal speed of this second species of ion in terms of uuu, giving your answer in its simplest surd form.