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An object is placed in front of a convex mirror at a distance of 60 m from its pole. Object starts moving towards the mirror at 20 ms1. Find the average speed of the image for a time interval of 2 s if the focal length of the mirror is 20 m.


Options:
A .   0.568 ms1
B .   1 ms1
C .   3 ms1
D .   2.5 ms1
Answer: Option D
:
D

Given: 
Initial object distance, u=60 m
Speed of object, vo=20 ms1
Focal length, f=20 m
Time interval, t=2 s
Applying mirror formula to find the initial position of the image v:
1v+1u=1f 
1v+160=120
v=15 m


Distance travelled by the object is the product of speed and time.
so=vot
so=20×2=40 m
Therefore, now the object distance: 
uf=u+so=60+40=20 m
Applying mirror formula to find the final position of the image vf:
1vf+1uf=1f 
1vf+120=120
vf=10 m
Average speed is the ratio of total distance travelled to the total time taken.
Average speed of the image:
vi=vvft
vi=15102=2.5 ms1



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