Question

A cyclist starts from the centre O of circular path of radius 10 m, covers the radius of circular path and reaches at point X on circumference, then cycles along the semi-circular path and reaches the point Y. If he takes 10 minutes to go from O to Y via X, then the net displacement and average speed of the cyclist would be........ANSWER IS (2)....EXPLAIN

Answer 1

Answer:  

The net displacement is 10 m and the ‘average speed’ of the cyclist is 0.069 m/s.

Solution:

The displacement is defined as the difference between final position and initial position irrespective of the route followed. As the question states, that the cyclist started from origin which is the centre of the circle and covered the distance of radius 10 m to reach the circumference of the circle. So, the initial position is the ‘centre of the circle’ let it be zero. After reaching the circumference, the cyclist travels the semicircular path and reaches Y, which means the cyclist covered the distance equal to the radius of the circle. So the final position is a point Y which is located diametrically opposite to the point X. Thus the displacement will be 10 m which is the difference between the final positions from centre i.e. equal to the radius of the circle. As the displacement does not count the route which the cyclist took so we can ignore the distance covered by the cyclist to reach the circumference of the circle from the ‘centre of the circle’.  

The average speed is

$\bold{\text {Average speed}=\frac{\text {Total distance}}{\text {Total time taken}}}$

In the total distance covered, the distance covered by the cyclist to reach the circumference of the circle from centre should be included. As the distance covered by the cyclist to reach the circumference of the circle from centre is equal to the ‘radius of the circle’.

$\text {Total distance covered}=\text {Radius of circle}+\text {Circumference of the semi circle}$

$\text {Total distance covered}=r+\pi r=10+(3.14 \times 10)$

$\text {Total distance covered}=10+31.4=41.4\ \mathrm{m}$

The total time taken is 10 min which is equivalent to 600 s. Thus the average speed is  

$\text {Average speed}=\frac{41.4}{600}=0.069\ \mathrm{m} / \mathrm{s}$

Thus the average speed is 0.069 m/s.

Answer 2

see the attachment to know the net displacement and average speed