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A particle moves along a straight line such that its displacement S varies with time ‘t’ as $S = α + β t + γ t^{2}$
Column – I Column - II
I) acceleration at $t = 2 s$ P) $β + 5 γ$
II) Average velocity during third second Q) $2 γ$
III) Velocity at $t = 1 s$ R) $α$
IV) initial displacement S) $β + 2 γ$

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I-Q, II-P, III-S, IV-R

I-Q, II-S, III-P, IV-Q

I-R, II-P, III-S, IV-Q

I-S, II-P, III-R, IV-S

answer is A.

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Detailed Solution

$v = \frac{d s}{d t} = β + 2 γ t a = \frac{d v}{d t} = 2 γ$ So, I-Q
$(v) = \frac{\int_{2}^{3} v d t}{\int_{2}^{3} d t} = \frac{β (3 - 2) + γ (9 - 4)}{1} = β + 5 γ$ So, II – P
Velocity at $t = 1 s : v = β + 2 γ \times 1 = β + 2 γ,$ So III – S
Initial displacement i.e., t = 0, S = a So, IV – R

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