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Question

For a car moving on a straight line with initial speed u, the minimum distance over which it can be stopped is s. If it's initial speed becomes nu, what will be the minimum distance over which it can be stopped? Assume constant braking force.

A
sn
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B
sn2
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C
ns
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D
n2s
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Solution

The correct option is D n2s
It's evident that car is in state of deceleration, and for constant braking force, acceleration (a)= constant
Since,
v2=u2+2as .....i
When car stops, final velocity v=0
0=u2+2as
a=u22s....ii
For the second case,
Initial velocity =nu
Final velocity v=0
From Eq. i:
0=(nu)2+2as
Substituting a from Eq. ii
n2u2=2×(u22s)×s
s=n2s
Hence s is the required minimum distance over which car will stop in second case.

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