The driver sitting inside a parked car is watching vehicles approaching from behind with the help of his side view mirror, which is a convex mirror with radius of curvature $R=2$ m. Another car approaches him from behind with a uniform speed of 90 km/hr. When the car is at a distance of 24 m from him, the magnitude of the acceleration of the image of the car in the side view mirror is ' a '. The value of $100a$ is _______ m/s².

Question

Dr. Abubacker · Accepted Answer

[Solution by Dr. Abubacker] $f=1$ m and the car's speed is $25$ m/s. With object distance $x$, the image distance is $v=\frac{xf}{x+f}$, so $\dot v=\frac{f^2}{(x+f)^2}\dot x$. With $\dot x$ constant, $a=\frac{2f^2\dot x^2}{(x+f)^3}=\frac{2(625)}{25^3}=0.08$ m/s², so $100a=8$. Answer: 8.

Explanation

Reviewed by Dr. Abubacker

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