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Question

A body falls from rest. In the last second of its fall n coven half of the total distance. If g is 9.8m/s2, then the total time of its fall is (in second)

A
2
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B
2+2
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C
22
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D
2±2
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Solution

The correct option is C 2±2
Let the total time taken by the body to fall be t.
Initial velocity of the body u=0m/s
Total distance traveled S=ut+12at2
S=12at2
Distance covered in last second, S=u+12a(2t1)
S=12a(2t1)
But S=12S
12a(2t1)= 14at2
We get t24t+2=0
t=4±(4)24(1)(2)2(1)
Or t=4±82
Or t=2±2

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