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(C) Given: Focal length $f = -25 \ cm$. Initial object distance $u_i = -50 \ cm$. Speed of object $v_o = 1 \ ms^{-1} = 100 \ cm s^{-1}$.At $t=0$,$u_i

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infinity

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(C) Given: Focal length $f = -25 \ cm$. Initial object distance $u_i = -50 \ cm$. Speed of object $v_o = 1 \ ms^{-1} = 100 \ cm s^{-1}$.At $t=0$,$u_i = -50 \ cm$. Using mirror formula $\frac{1}{v} + \frac{1}{u} = \frac{1}{f}$,we get $\frac{1}{v_i} + \frac{1}{-50} = \frac{1}{-25} \implies \frac{1}{v_i} = -\frac{1}{25} + \frac{1}{50} = -\frac{1}{50} \implies v_i = -50 \ cm$.At $t=0.25 \ s$,the distance moved by the object is $d = v_o 	imes t = 100 \ cm s^{-1} 	imes 0.25 \ s = 25 \ cm$.New object distance $u_f = -50 \ cm + 25 \ cm = -25 \ cm$.Since the object is at the focus,the image is formed at infinity,i.e.,$v_f = \infty$.The average velocity of the image is $\langle v angle = \frac{v_f - v_i}{\Delta t} = \frac{\infty - (-50)}{0.25} = \infty$.

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