Two particles \(A\) and \(B\) move from rest along a straight line with constant accelerations \(f\) and f' respectively. If \(A\) takes \(\mathrm{m}\) sec. more than that of \(\mathrm{B}\) and describes \(\mathrm{n}\) units more than that of \(\mathrm{B}\) in acquiring the same velocity, then
(A) \(\left(f+f^{\prime}\right) m^{2}=f f^{\prime} n\)
(B) \(\left(f-f f^{\prime}\right) m^{2}=f f^{\prime} n\)
(C) \(\left(f^{\prime}-f\right) n=\frac{1}{2} f f^{\prime} m^{2}\)
(D) \(\frac{1}{2}\left(f+f^{\prime}\right) m=f f^{\prime} n^{2}\)