Question

Rohit completes a semicircular path of radius \(\mathrm{R}\) in 10 seconds. Calculate average speed and average velocity in \(\mathrm{ms}^{-1}\) (A) \([(2 \pi R) / 10],(2 R / 10)\) (B) \((\pi R / 10),(\mathrm{R} / 10)\) (C) \((\pi R / 10),(2 R / 10)\) (D) \([(2 \pi R) / 10],(\mathrm{R} / 10)\)

Short answer

The short answer is: (C) \((\pi R / 10),(2 R / 10)\).

Step-by-step solution

Find Distance Covered by Rohit

The distance is the total length of the semicircular path Rohit travels. The formula for the circumference of a circle is \(2\pi{R}\), so for a semicircle, the distance would be half of this, which is $$ D = (\pi R). $$

Find Displacement of Rohit

Displacement is the straight distance from Rohit's starting point to his endpoint. Rohit begins at one end of the semicircle and takes a straight line to the other end, which is equivalent to the diameter of the semicircular path. The formula for diameter is 2R. Thus, the displacement is $$ s = 2R. $$

Calculate Average Speed

To find the average speed, we need to divide the total distance traveled by the time taken. In this case, the time taken is given as 10 seconds. Therefore, the average speed would be represented as $$ v_{avg(speed)} = \frac{D}{t} = \frac{\pi R}{10}. $$

Calculate Average Velocity

To find the average velocity, we need to divide the total displacement by the time taken. In this case, the time taken is also given as 10 seconds. Therefore, the average velocity would be represented as $$ v_{avg(velocity)} = \frac{s}{t} = \frac{2R}{10}. $$

Compare Answers to Given Options

Comparing our calculated average speed and average velocity to the given options, we get: (A) \([(2 \pi R) / 10],(2 R / 10)\) (B) \((\pi R / 10),(\mathrm{R} / 10)\) (C) \((\pi R / 10),(2 R / 10)\) (D) \([(2 \pi R) / 10],(\mathrm{R} / 10)\) So, the correct answer to the problem is (C) \((\pi R / 10),(2 R / 10)\).