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Question

A car, moving at 1.5 ms1 applies brakes and comes to rest in 2s. If the same car travels at double the speed, what time would it take to come to rest after applying brakes?

A
4s
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B
8s
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C
2s
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D
3s
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Solution

The correct option is A 4s
Given,
Initial velocity u1=1.5ms1
Final velocity v1=0
Time taken t1=2s

According to first equation of motion,
v1=u1+a1t1
0=1.5+2a1
a1=1.52=0.75 ms2

Now, for the second case,
Initial velocity u2=3ms1
Final velocity v2=0
The braking system is still the same. So it provides the same retarding acceleration of 0.75 ms1
So acceleration a2 is same as a1=0.75 ms1
Using first equation of motion again,
v2=u2+a1t2
0=30.75×t2
t=30.75=4s

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