Let the circular path have radius R. The circumference is $C = 2\pi R$. The distance covered by the person is half the circumference, $d = \frac{1}{2} C = \pi R$. Let the time taken be $t$. Average speed is defined as the total distance traveled divided by the total time taken. Average speed = $\frac{d}{t} = \frac{\pi R}{t}$.The person moves along a circular path by a distance equal to half the circumference. This means the person starts at one point on the circle and ends at the diametrically opposite point. Let the starting point be A and the ending point be B, where AB is a diameter of the circle. The displacement is the shortest straight-line distance from the initial position to the final position. In this case, the displacement is the length of the diameter. Displacement = $2R$.Average velocity is defined as the total displacement divided by the total time taken. Average velocity = $\frac{\text{Displacement}}{t} = \frac{2R}{t}$.The ratio of average speed to average velocity is: Ratio = $ \frac{\text{Average speed}}{\text{Average velocity}} = \frac{\pi R / t}{2R / t} = \frac{\pi R}{t} \times \frac{t}{2R} = \frac{\pi}{2}$. The value $ \frac{\pi}{2}$ is equivalent to $0.5\pi$.
A person moves along a circular path by a distance equal to half the circumference in a given time. The ratio of his average speed to his average velocity is :
Asked in UPSC CAPF 2009 · Topic: Mechanics (Newton's Laws of Motion and their applications)
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