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# Derive an expression for displacement in the last or nth second

Asked by Paitboy23 26th June 2019, 5:44 AM
Let u be the initial velocity and a is acceleration.

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To get velecity V after T seconds we use the formula, V = U+A×T , where A is acceleration
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Hence velocity after (n-1) seconds = u+(n-1)×a .........................(1)

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To get displacement S after T seconds, we use the formula,  S = U×T + (1/2)×A×T2 ,
where U is initial velocity and A is acceleration
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Hence displacement Sn at nth or last second is obtained by using the intial velocity from eqn.(1) and it is given by,

Sn = u+(n-1)×a +(1/2)×a×1 = u+a×[ n- (1/2) ]
Answered by Expert 26th June 2019, 11:06 AM
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