Two particles move in the same straight line | vedclass

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(B, C) Let $S_1$ be the displacement of the first particle and $S_2$ be the displacement of the second particle at time $t$.For the first particle: $S

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their greatest distance is $\frac{u^{2}}{2 f}$

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(B, C) Let $S_1$ be the displacement of the first particle and $S_2$ be the displacement of the second particle at time $t$.For the first particle: $S_1 = u t$.For the second particle: $S_2 = \frac{1}{2} f t^2$.The distance between them is $D(t) = |S_1 - S_2| = |u t - \frac{1}{2} f t^2|$.To find the greatest distance, we differentiate $D(t)$ with respect to $t$ and set it to zero:$\frac{dD}{dt} = u - f t = 0$.This gives $t = \frac{u}{f}$.At $t = \frac{u}{f}$, the distance is $D = u(\frac{u}{f}) - \frac{1}{2} f(\frac{u}{f})^2 = \frac{u^2}{f} - \frac{u^2}{2f} = \frac{u^2}{2f}$.Thus, the particles are at the greatest distance at $t = \frac{u}{f}$ and the maximum distance is $\frac{u^2}{2f}$.Therefore, options $B$ and $C$ are correct.

Two particles move in the same straight line starting at the same moment from the same point in the same direction. The first moves with constant velocity $u$ and the second starts from rest with constant acceleration $f$. Then,

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