First slide

Relative velocity in 1-d

Question

Two trains travelling on the same track are approaching each other with an equal speed of 40 m/s. The drivers of the trains begin to decelerate simultaneously when they are just 2 km apart. Assuming the deceleration to be uniform and equal , the value of the deceleration to barely avoid collision should be …..in m/ $s^{2}$

Moderate

A

0.2
B

0.6
C

0.4
D

0.8

Solution

initial relative velocity of first train with respect second train=80 m/s
final relative velocity of 1 ^st train w.r.t 2 ^nd train =0
relative deceleration = -2a
relative distance=2000 m
v ²-u ²=2 a s
(0)² -(80) ²=2(-2 a)2000
a=0.8 m/ s²

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