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(B) The man is running with a constant speed along a circular path. In uniform circular motion,the speed of the object remains constant at all points

Vedclass · Accepted Answer

$\frac{2 \sqrt 2 \pi}{5} \, m/s$

Vedclass · Answer

(B) The man is running with a constant speed along a circular path. In uniform circular motion,the speed of the object remains constant at all points on the path. The radius of the path is $r = 2 \sqrt 2 \, m$. The time taken to complete one round (period) is $T = 10 \, s$. The distance covered in one round is the circumference of the circle,$C = 2 \pi r$. $C = 2 \pi (2 \sqrt 2) = 4 \sqrt 2 \pi \, m$. The constant speed $v$ is given by the ratio of total distance to total time: $v = \frac{C}{T} = \frac{4 \sqrt 2 \pi}{10} = \frac{2 \sqrt 2 \pi}{5} \, m/s$. Since the speed is constant,the instantaneous speed at any time $t$,including $t = 2.5 \, s$,is the same as the average speed. Therefore,the instantaneous speed is $\frac{2 \sqrt 2 \pi}{5} \, m/s$.

$A$ man is running with constant speed along a circular path of radius $2 \sqrt 2 \, m$. He completes $1$ round in $10 \, s$. Find the instantaneous speed at $2.5 \, s$.

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