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A particle moving along a straight line with initial velocity u and acceleration a continuous its motion for n seconds. What is the distance covered by it in the last nth second?

Text Solution

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`S=ut+(1)/(2)at^(2)`
Displacement in n seconds `=un+(1)/(2)an^(2)`
Displacement in `(n-1)` seconds
`=u(n-1)+(1)/(2)a(n-1)^(2)`
Displacement in `n^(th)` second = Displacement in n secons - displacement in `(n-1)` seconds.
`therefore S_(n)=u+a(n-(1)/(2))`.
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