A train is moving at a constant speed V. When its driver observes… - Vidyadip

MCQ

A train is moving at a constant speed $V$. When its driver observes another train in front of him on the same track and moving in the same direction with constant speed $u$. If the distance between the trains be $x$, then what should be the minimum retardation of the train so as to avoid collision?

A
$(V + u)^2\,/x$
B
$(V -u)^2\,/x$
C
$(V + u)^2\,/2x$
✓
$(V -u)^2\,/2x$

✓

Answer

Correct option: D.

$(V -u)^2\,/2x$

d
Here relative velocity of the train $w.r.t.$ other

$\operatorname{train}=V-u$

Hence,

$0-(\mathrm{V}-\mathrm{u})^{2}=2 \mathrm{ax}$ or $\mathrm{a}=-\frac{(\mathrm{V}-\mathrm{u})^{2}}{2 \mathrm{x}}$

Minimum retardation $=\frac{(\mathrm{V}-\mathrm{u})^{2}}{2 \mathrm{x}}$

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