The position of a mirror and a particle moving along X-axis is given by x m = t 3 − 6 t 2 and x p = 9 t 2 − 60 t . Match the List-I with List-II. List-I List-II (I) Velocity of image of particle i

Question

The position of a mirror and a particle moving along X-axis is given by $x_{m} = t^{3} - 6 t^{2}$ and $x_{p} = 9 t^{2} - 60 t$ . Match the List-I with List-II.

List-I	List-II
(I) Velocity of image of particle is zero	(P) 2 sec
(II) Acceleration of image of particle is zero	(Q) 3 sec
(III) Acceleration of image of particle is negative	(R) 3.5 sec
(IV) Velocity of image of particle is towards the origin	(S) 4 sec
	(T) 5 sec

TestHub · Accepted Answer

Velocity of the image: v img ​ = ( 6 t 2 − 24 t ) − ( 18 t − 60 ) = 6 t 2 − 42 t + 60 = 6 ( t − 2 ) ( t − 5 ) (I) v_img = 0 at t = 2 sec and t = 5 sec → P, T (II) a img ​ = 12 t − 42 = 0 ⇒ t = 3.5 sec → R (III) a_img < 0 ⇒ t < 3.5 sec ⇒ t = 2, 3 sec → P, Q (IV) v_img < 0 at t = 3, 3.5, 4 sec, so the image moves towards the origin → Q, R, S I → P,T; II → R; III → P,Q; IV → Q,R,S, so option (A) is correct.

Physics - Geometrical Optics Question with Solution | TestHub

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