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(n−1)n
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D
2v(n−1)n
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Solution
The correct option is D2v(n−1)n The distance travelled by the particle in the last 2 seconds = distance travelled by nth second −distance travelled by (n−2)th second.
∵v=0+na⇒a=vn ∴ displacement in last two seconds, =Sn−Sn−2=12an2−12a(n−2)2 =a2[n2−(n−2)2]=a2[n+(n−2)][n−(n−2)] =a(2n−2)=vn(2n−2)=2v(n−1)n.