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A body is moving from rest under constan...

A body is moving from rest under constance accelration and let `S_1` be the displacement in the first `(p-1)` sec and `S_2` be the displacement in the first p sec. The displacement in `(p^2-p+1)^(th)` sec will be

A

`S_(1)+S_(2)`

B

`S_(1)S_(2)`

C

`S_(1)-S_(2)`

D

`S_(1)//S_(2)`

Text Solution

Verified by Experts

The correct Answer is:
A
From the second equation of motion we know that
`S=ut +(1)/(2) at^(2)`
In p - 1 seconds
`S_(1)=(1)/(2) a(P-1)^(2)`
and in p seconds
`S_(2)=(1)/(2) aP^(2)` [As u = 0]
With above equations we know that
`S_(1)+S_(2)=(1)/(2)a(2p^(2)-2p+1)`
From the displacement formula of nth second we know that `S_(n) = u+(a)/(2) (2n-1)`
`S_((P^(2)-P+1)^(th))=(a)/(2)[2(P^(2)-P+1)-1]`
`=(a)/(2) [2P^(2)-2P+1]`
It is clear that `S_((P^(2)+P+1)^(th))=S_(1)+S_(2)`
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