A sportsman runs around a circular track of radius 
such that he traverses the path 
. The distance travelled and displacement, respectively, are
Text Solution
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To determine the distance traveled and displacement of a sportsman running around a circular track, we begin by analyzing the path described as 
.
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 
back to 
) and then continues to point 
(which is opposite point 
on the circle). Therefore, the displacement is the diameter of the circle:
Displacement 
Distance:
The distance is the total path length traveled by the sportsman. Starting at 
, he completes one full circle back to 
, which has a circumference of:
He then runs half the circle from 
to 
, which is another:
Thus, the total distance is the circumference of
the full circle plus half of another circle: Distance 
In summary, the distance traveled by the sportsman is 
and the displacement is 
.
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