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 v≥√2ad
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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 v≤√ad
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Solution
The correct options are A The man catches the bus if v≥√2ad 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 12at2−vt+d=0 Solution of above equation is t=v±√v2−2ada this t should be real for man to catch the bus so v2−2ad>0⇒v>√2ad If the man just catches the bus then relative velocity of man wrt bus is zero, at that instant. Vmb=Umb+ambt 0=v−at ∴t=(va)