A car fitted with a convex …

Ans.

Object Distance (u) = -2.8 m = -280 cm

Focal Lenght of Mirror (f) = 20 cm

Velocity of Object = \(({du\over dt}) = \)  15 m/s =  1500cm m/s

We Know Mirror Formula :

\({1\over v } + {1\over u } = {1\over f}\) 

=> \({1\over v } - {1\over 280 } = {1\over 20}\)

=> \({1\over v } = {1\over 20} + {1\over 280 } \)

=> \(v = {280\over 15} \)

Again

\({d\over dt}{({1\over v } + {1\over u }}) = {d\over dt}({1\over f})\)

=> \(-{1\over v^2}{dv\over dt} - {1\over u^2}{du\over dt} = 0\)

=> \({1\over v^2}{dv\over dt} =-{1\over u^2}{du\over dt}\)

=> \({dv\over dt} = -{v^2\over u^2}{du\over dt}\)

Put Values of All, We get 

=> \({dv\over dt} = -{{({280\over 15})^2}\over{ 280^2}} \times 1500 = {-1500\over 225} = -100/15 \space cm/s\)

=> \({dv\over dt}= -{1\over 15} \space m/s\)

-ve sign implies that image appears to be opposite to that of the object.

So, velocity of Image =\(-{1\over 15}m/s\)