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Question

A man is d distance behind a bus. The bus starts moving away from the man with an acceleration a. At the same time man starts running towards the bus with a constant velocity v.

A
The man catches the bus if v2ad
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B
If man just catches the bus, the time of catching the bus will be t=va
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C
If man just catches the bus, the time of catching the bus will be t=2va
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D
The man will catch the bus if vad
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Solution

The correct options are
A The man catches the bus if v2ad
B If man just catches the bus, the time of catching the bus will be t=va


Let the man catches the bus after time t. Distance travelled by the bus in time t
s1=12at2
Distance travelled by the man in time t
s2=vt
The passenger will catch the bus if,
d+s1=s2
d+12at2=vt
12at2vt+d=0
Solution of above equation is
t=v ± v22ada
this t should be real for man to catch the bus so
v22ad>0v>2ad
If the man just catches the bus
then relative velocity of man wrt bus is zero, at that instant.
Vmb=Umb+ambt
0=vat
t=(va)

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