First slide

Relative velocity in 1-d

Question

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 v.
If the distance between the trains is x, then what should be the minimum retardation of the train so as to avoid collision?

Moderate

A

$\frac{(V + v)^{2}}{x}$
B

$\frac{(V - v)^{2}}{x}$
C

$\frac{(V + v)^{2}}{2 x}$
D

$\frac{(V - v)^{2}}{2 x}$

Solution

Here relative velocity of the train w.r.t. other train is
$\begin{array}{l} V - v . Hence, 0 - (V - v)^{2} = 2 a x \\ or a = - \frac{(V - v)^{2}}{2 x} Minimum retardation = \frac{(V - v)^{2}}{2 x} \end{array}$

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