Question

An athlete completes one round of a circular track of diameter $200m$ in $40s$ What will be the distance covered and the displacement at the end of $2min.20s.$

Answer 1

Step 1. Given data:

Diameter of circular track = $200m$

Time taken = $40s$

Time taken (Final)=$2min20s$

Step 2. Formula used:

Circumference of circle = $2\mathrm{\pi r}$, where $r=$radius of the circle.

Step 3. Calculations:

Distance covered in one complete oscillation = Circumference of circular track

Thus,
Distance covered in $40s=2\times \mathrm{\pi }\times 100=628\mathrm{m}$….As radius $r=\raisebox{1ex}{$D$}\!\left/ \!\raisebox{-1ex}{$2$}\right.=\raisebox{1ex}{$200$}\!\left/ \!\raisebox{-1ex}{$2$}\right.=100m$

Distance covered in$1s=\raisebox{1ex}{$628$}\!\left/ \!\raisebox{-1ex}{$40$}\right.=15.7m$

Total time in seconds in final timer taken = $2min20sec.=140sec.$

Thus, the distance covered in $140sec.=15.7\times 140=2198m\cong 2200m$

Displacement in $2min.$ that is $120sec.$ will be zero because the athlete will complete $3$ rounds and at that time initial position and final position will be the same. But, later the next $20sec$ the displacement will be equal to the diameter of the circular track which is $200m$.

Thus, the distance covered = $2200m$ and the displacement = $200m$.