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A particle moves on a line by $S = l t^{2} + m t + n .$ If the displacement after 1 second is 16 cm. The velocity of after 2 seconds is $24 c m / \sec$ and the acceleration is $8 {cm/sec}^{2}$ then $(l, m, n) =$

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(8, 8, 4)

(8, 4, 4)

(4, 8, 4)

(4, 4, 8)

answer is A.

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Detailed Solution

$S = ℓ t^{2} + m t + n$

at $t = 1, ℓ + m + n = 16$

$v = 2 ℓ t + m$

$t = 2,$ $v = 4 ℓ + m = 24$

a= 2 l

$a = 2 ℓ = 8$

$ℓ = 4$

$m = 8, n = 4$

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