Question

A cyclist moving on a circular track of radius $ 100m $ completes one revolution in $ 4\min $ . What is his: $ (i) $ average speed.
 $ (ii) $ average velocity in one full revolution.

Answer 1

Hint :In this question we have been given the radius of the track followed by the cyclist. From the radius of the circular track we can find out the distance i.e. circumference of the circular track which is followed by the cyclist in one revolution. Average speed is the ratio of total distance travelled with respect to total time taken.

Complete Step By Step Answer:
As per the given data we have the radius of the circular track and time taken by the cyclist to complete one revolution. Thus, $ r = 100m $ which is the radius of the circle and time taken for completing one revolution is $ t = 4\min $ .
Now circumference of the circle is given by:
 $ C = 2\pi r $
Putting all the values we get,
 $ C = 2\pi (100) $
 $ \Rightarrow C = 200\pi $ (in meter)
 $ (i) $ for average speed
Average speed is the ratio of total distance travelled with respect to total time taken.
Let $ {v_{avg}} $ be the average speed of the cyclist.
Now, $ {v_{avg}} = \dfrac{{circumference}}{{time}} $ ………(circumference is equal to total distance travelled in one revolution)
Time taken is $ t = 4\min $
Therefore, put these values in the above equation we get,
 $ \Rightarrow {v_{avg}} = \dfrac{{200\pi }}{4} $
 $ \Rightarrow {v_{avg}} = 50\pi m{s^{ - 1}} $
Thus the average speed is calculated as $ 50\pi m{s^{ - 1}} $
 $ (ii) $ Average velocity is the ratio of displacement of an object with respect to time
In circular motion the displacement is $ zero $ because the displacement is defined as the change in position of an object, but in this kind of motion the cyclist is coming back to its own position after travelling the whole circle. So the displacement here is $ zero $ and average velocity is also termed as $ zero $ .

Note :
Average speed and average velocity are two different terms. Average speed dependent on distance and average velocity is dependent on displacement. Distance is termed as the total covered path by an object and displacement is termed as change in position of the object. Hence, be careful when you solve these types of questions.