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Question

A body starts from rest with a uniform acceleration. If its velocity after n second is v, then its displacement in the last 2 s is

A
2v(n+1)n
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B
v(n+1)n
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C
v(n1)n
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D
2v(n1)n
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Solution

The correct option is D 2v(n1)n
By using first equation of motion
v=0+na (u=0)
a=vn
Displacement covered in n seconds is
Sn=12an2 and distance travelled in (n2) seconds is
Sn2=12a(n2)2
So, displacement travelled in the last 2 s is
SnSn2=12an212a(n2)2
=a2[n2(n2)2]
SnSn2=a2(n2n24+4n)=2a(n1)
SnSn2=2v(n1)n

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