Question

An object is placed in front of a convex mirror at a distance of $60m$ from its pole. Object starts moving towards the mirror at $20m{s}^{-1}$. Find the average speed of the image for a time interval of $2s$ if the focal length of the mirror is $20m$.

• A. $0.568m{s}^{-1}$
• B. $1m{s}^{-1}$
• C. $3m{s}^{-1}$
• D. $2.5m{s}^{-1}$

Answer 1

The correct option is D

$2.5m{s}^{-1}$

Given:
Initial object distance, $u=-60m$
Speed of object, $v_o=20m{s}^{-1}$
Focal length, $f=20m$
Time interval, $t=2s$

Applying mirror formula to find the initial position of the image $v$:
$\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$
$\frac{1}{v}+\frac{1}{-60}=\frac{1}{20}$
$v=15m$

Distance travelled by the object is the product of speed and time.
$s_o=v_{o}t$
$s_o=20\times 2=40m$

Therefore, now the object distance:
$u_f=u+s_o=-60+40=-20m$

Applying mirror formula to find the final position of the image $v_f$:
$\frac{1}{v_f}+\frac{1}{u_f}=\frac{1}{f}$
$\frac{1}{v_f}+\frac{1}{-20}=\frac{1}{20}$
$v_f=10m$

Average speed is the ratio of total distance travelled to the total time taken.
Average speed of the image:
$v_i=\frac{v-v_f}{t}$
$v_i=\frac{15-10}{2}=2.5m{s}^{-1}$