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Question

A bus moving on a level road with a velocity V can be stopped at a distance of x, by the application of a retarding force F. The load on the bus is increased by 25% by boarding the passengers. Now, if the bus is moving with the same speed and if the same retarding force is applied, the distance travelled by the bus before it stops is:

A
1.25x
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B
x
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C
5x
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D
2.5x
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Solution

The correct option is A 1.25x
Let the mass of the system be m
Initial velocity of bus u=V
Final velocity of bus v=0
Acceleration of the bus a=Fm
Using v2u2=2aS
0V2=2×(Fm)×x V2=2Fxm ...........(1)

Now the mass of the system is increased by 25 %
New mass of the system M=1.25m
Acceleration of bus a=F1.25m
Using v2u2=2ax
0V2=2×(F1.25m)×x V2=2Fx1.25m .....(2)

From (1) and (2) we get 2Fx1.25m =2Fxm
x=1.25x

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