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Question

A body starts from rest with uniform acceleration and remains in motion for n seconds. If its final velocity after n second is v, then its displacement in the last two seconds will be

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
The distance travelled by the particle in the last 2 seconds = distance travelled by nth second distance travelled by (n2)th second.

v=0+naa=vn
displacement in last two seconds,
=SnSn2=12an212a(n2)2
=a2[n2(n2)2]=a2[n+(n2)][n(n2)]
=a(2n2)=vn(2n2)=2v(n1)n.


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