Question
A runner completes one round of a circular track of diameter 400 m in 40 s. What will be the distance covered and the displacement respectively at the end of 2 minutes 20 s?
Answer: Option B
:
B
Given:
Diameter of the circle, d=400m
Time taken to complete one circle, T=40s
Total time of motion, T2=2min20s
Circumference of circle, C=πd
Speed is defined as the ratio of distance covered to time taken.
Hence, speed of the runner
v=CT=πdT
Total time of motion, T2=2min20s=140s
Total distance covered is given by:
D=vT2
D=πdT2T
D=π×400×14040
D≈4400m
No. of rounds completed:
n=Total distance coveredCircumference of the circle
n=Dπd
n=T2T
n=140040=3.5
This means that he will be at the diametrically opposite end, i.e., he starts at A and ends at B.
Hence displacement, s=2r=400m
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:
B
Given:Diameter of the circle, d=400m
Time taken to complete one circle, T=40s
Total time of motion, T2=2min20s
Circumference of circle, C=πd
Speed is defined as the ratio of distance covered to time taken.
Hence, speed of the runner
v=CT=πdT
Total time of motion, T2=2min20s=140s
Total distance covered is given by:
D=vT2
D=πdT2T
D=π×400×14040
D≈4400m
No. of rounds completed:
n=Total distance coveredCircumference of the circle
n=Dπd
n=T2T
n=140040=3.5
This means that he will be at the diametrically opposite end, i.e., he starts at A and ends at B.
Hence displacement, s=2r=400m
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