Prove that when two trains move in the opposite direction, then one train appears to move faster than its actual - Physics - Motion In A Straight Line

Question

Prove that when two trains move in the opposite direction, then one
train appears to move faster than its actual speed of the other
train

Satyendra Singh · Accepted Answer

Dear Student,
Please find below the solution to the asked
query:

let us consider two trains on moving due east with a magnitude of
velocity of '|ve =v|' and the other is moving west with
a magnitude '|vw = v|' Now,

the since the trains move in opposite direction then, ve
= -vw

Now,

suppose one of trains comes to a halt and the velocity vector of it
is added to the other train Then the person on the stationary train
will be able to see the other train exactly at the same speed as
earlier Then,

vtrain for observer = ve - vw (
since both are in opposite direction hence the
'-ive' sign as then they will follow the rules of
vector addition)
vtrain
for
observer = v - (-v) = -2v
â€‹since 2v > v

thus we conclude that for two trains moving in opposite
directions 
then one train appears to move faster than its actual speed of the
other train

Hope this
information will clear your doubts about (Motion)
If you have any more doubts just ask here on the forum and our
experts will try to help you out as soon as possible
Regards
Satyendra Singh

Prove that when two trains move in the opposite direction, then one train appears to move faster than its actual speed of the other train.