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The equation of motion of particle is described in column-I. At t = 0 particle is at origin and at rest
Column I Column II
A) $x = 3 t^{2} + 2 t$ P) Velocity of particle at t = 1sec is 8m/s
B) $v = 8 t$ Q) Particle moves with uniform acceleration
C) $a = 16 t$ R) Particle moves with variable acceleration
D) $v = 6 t - 3 t^{2}$ S) Acceleration of the particle at t = 1 is 2m/s²
T) Particle will change its direction of motion

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$A \to P, Q; B \to P, Q; C \to P, T; D \to R, T$

$A \to P, R; B \to P, Q; C \to P, R; D \to R, T$

$A \to P, Q; B \to P, R; C \to P, R; D \to R, T$

$A \to P, Q; B \to P, Q; C \to P, R; D \to R, T$

answer is D.

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Detailed Solution

$A) x = 3 t^{2} + 2 t; v = 6 t + 2 . . . . . . (1)$

$put t = 1; v = 8 m / \sec$

$\frac{dv}{dt} = a \Rightarrow a = 6 m / \sec^{2} (time independent)$

$B) v = 8 t; put t = 1 \Rightarrow v = 8 m / \sec$

$\frac{dv}{dt} = a = 8 m / \sec^{2}' a' is constant$

$C) \frac{dv}{dt} = a = 16 t; dv = (16 t) dt$

$v = \frac{16 t^{2}}{2} = 8 t^{2}, put t = 1 \Rightarrow v = 8 m / \sec$

$\frac{dv}{dt} = a = 8 t, If ' t' varies ' a' also varies$

$D) v = 6 t - 3 t^{2}; a = \frac{d v}{d t} = 6 - 6 t$

‘a’ is variable and after some time particle changes its direction motion

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Column I	Column II
A) $x = 3 t^{2} + 2 t$	P) Velocity of particle at t = 1sec is 8m/s
B) $v = 8 t$	Q) Particle moves with uniform acceleration
C) $a = 16 t$	R) Particle moves with variable acceleration
D) $v = 6 t - 3 t^{2}$	S) Acceleration of the particle at t = 1 is 2m/s²
	T) Particle will change its direction of motion