Question

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

Answer 1

Step 1: Given data:

1. Diameter of the circular track = 200 m
2. Time taken to complete one round = 40s

Step 2: Formula

$Circumferenceofthecirculartrack=2\mathrm{\pi r}$

Where r is the radius of the circular track and $\mathrm{\pi }=\frac{22}{7}$

$Circumferenceofthecirculartrack=2\mathrm{\pi r}=2\times \frac{22}{7}\times 100=\frac{4400}{7}m$

Step 3:Finding the speed:

$Speed=\frac{Dis\tan cecovered}{Timetaken}$

$\frac{Dis\tan cecovered}{Timetake}=\frac{4400}{40\times 7}=\frac{110}{7}m/s$

Step 4:Finding the distance traveled:

Therefore, distance traveled in 2 minutes and 20s or in 140 seconds will be,

$Speed\times Time=\frac{110}{7}\times 140=2200m$

Step 5: Finding the displacement:

1. After every 40 sec, the athlete reaches his starting point. So after 40 sec, his displacement is zero.
2. Thus, the athlete completes the circular track 3 times in the 120 sec, and in the next 20 sec, he is just opposite to his starting point.

Therefore, the magnitude of the displacement of the athlete at the end of the 140 seconds = Diameter of track = 200 m.