Question 33: Work, Energy and Power & Circular Motion

Question

A sportsman runs around a circular track of radius $r$ such that he traverses the path $A B A B$. The distance travelled and displacement, respectively, are

Accepted Answer

To determine the distance traveled and displacement of a sportsman running around a circular track, we begin by analyzing the path described as $ A ightarrow B ightarrow A ightarrow B $.
Displacement:
The displacement is the straight line distance from the initial point to the final point. In this case, the sportsman completes one full circle (from $ A $ back to $ A $) and then continues to point $ B $ (which is opposite point $ A $ on the circle). Therefore, the displacement is the diameter of the circle:
$ 	ext{Displacement} = 2r $
Distance:
The distance is the total path length traveled by the sportsman. Starting at $ A $, he completes one full circle back to $ A $, which has a circumference of:
$ 2 \pi r $
He then runs half the circle from $ A $ to $ B $, which is another:
$ \frac{1}{2} 	imes 2 \pi r = \pi r $
Thus, the total distance is the circumference of the full circle plus half of another circle:
$ 	ext{Distance} = 2 \pi r + \pi r = 3 \pi r $
In summary, the distance traveled by the sportsman is $ 3\pi r $ and the displacement is $ 2r $.

Answer

$\pi r, 3 r$

Answer

$2 \mathrm{r}, 3 \pi \mathrm{r}$

Answer

$3 \pi \mathrm{r}, 2 \mathrm{r}$

Answer

$3 \pi r, \pi r$

Work, Energy and Power & Circular Motion

A sportsman runs around a circular track of radius r such that he traverses the path A B A B. The distance travelled and displacement, respectively, are

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