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(B) The distance between the two particles is given by $s = s_1 - s_2$,where $s_1 = ut$ and $s_2 = \frac{1}{2}ft^2$.$s = ut - \frac{1}{2}ft^2$.To find

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$\frac{u^2}{2 f}$

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(B) The distance between the two particles is given by $s = s_1 - s_2$,where $s_1 = ut$ and $s_2 = \frac{1}{2}ft^2$.$s = ut - \frac{1}{2}ft^2$.To find the maximum distance,we differentiate $s$ with respect to $t$ and set it to zero:$\frac{ds}{dt} = u - ft = 0 \implies t = \frac{u}{f}$.At this time $t = \frac{u}{f}$,the velocity of the second particle equals the velocity of the first particle.Substituting $t = \frac{u}{f}$ into the expression for $s$:$s_{\max} = u(\frac{u}{f}) - \frac{1}{2}f(\frac{u}{f})^2$$s_{\max} = \frac{u^2}{f} - \frac{u^2}{2f} = \frac{u^2}{2f}$.

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