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# ​Q. A MAN IS ‘L’=9 m BEHIND THE DOOR OF A TRAIN WHEN IT STARTS MOVING WITH ACCELERATION a=2m/s2. THE MAN RUNS AT FULL SPEED. HOW FAR DOES HE HAVE TO RUN AND AFTER WHAT TIME HE GET INTO THE TRAIN? WHAT IS HIS FULL SPEED?

shashi K Sharma
46 Points
6 years ago
Dear Student
There is a huge conceptual error with the author of the question who thinks that the train can be boarded only when the speed of the body say v equals the speed of train, but blv me theres no such contraint practically;
Anyhow let us honour the question then speed of body v= speed of train at the time of boarding say at time t
hence v = at   or v=2t
also the man travels a distance vt in time t which should be equal to the gap of 9m plus the distance moved by train in time t(which is 1/2at^2)
i.e. vt = 9 + 1/2at^2
replacing v=2t and a=2 we get
2t^2 = 9 + t^2
or t=3

hence vt =
shashi K Sharma
46 Points
6 years ago
thus full speed v = at
or v = 6m/s
Bharat Makkar
34 Points
6 years ago
thanks sir
Richik
11 Points
4 years ago
Sir i have  a doubt.sir,is it necessary that the time instant when the man will attain the velocity of the train will be the time instant where he covers the distance of the train +9m because that is what u have done.
V=2t will be valid only for a particular time instant and that need not be the time in which man will cover the distance s +9m.Please clarify