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Question

a person travellingwith you in a bus is at rest . do you agree with the statement ?

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Solution

No.Because when we check his position at two different time,it is not same.so change in position means he is not a rest.But when thinking in concept of resultant velocity, i.e when considering the person with respect to bus,he is at rest.It is because both man and bus is moving at same velocity. Thus resultant velocity of man with respect to bus=v of man -v of bus =0....
so he is in rest when comparing with bus.
He is also respect with respect to us,bcz our velocity is also same as velocity of vehicle which is equal to velocity of that man.so he is also at rest withrespect to us....

He is not rest when thinking in independent sense.

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