Question

An athlete completes one round of a circular track of diameter $200m$ in $40s$. If he continues to run, what will be the distance covered and the displacement at the end of $2$ minutes $20s$ respectively ?

• A. $2200m,200m$
• B. $2200m,0m$
• C. $4400m,400m$
• D. $2200m,400m$

Answer 1

The correct option is A

$2200m,200m$

Explanation for the correct option:

Step 1: Given data in the question.

In the question, it is given that, An athlete completes one round of a circular track of diameter $200m$ in $4s$.

Step 2: Concept and formula to be used.

1. The length of the circumference $l$ of the circle when the diameter $d$ is given can be calculated as follows: $l=\pi d$
2. When the distance $D$ and time $T$ is given then the speed $S$ can be calculated as follows: $S=\frac{D}{T}$
3. According to the definition of displacement, displacement is defined as the shortest distance between the initial point and the final point.
4. When the time $T$ of completing one round and the time $t$ at which the number of rounds to be calculated is given. Then the number of rounds $n$ can be given by: $n=\frac{t}{T}$.

Step 3: Find the required distance and displacement.

Find the length $l$ of the circumference of the track.

$$\begin{gathered} l=\mathrm{\pi }·200 \\ \Rightarrow \mathrm{l}=628.31 \end{gathered}$$

That means the athlete completes one round of the track of length $628.31m$ in $40s$.

So, the speed $s$ of the athlete is given as follows:

$$\begin{gathered} s=\frac{628.31}{40} \\ \Rightarrow s=15.70 \end{gathered}$$

Therefore, the speed of the athlete is $15.70m/s$.

Now, find the distance $d$ travelled by the athlete in $2$ minutes $20s$.

Since, $2$ minutes $20s$ is equal to $140s$.

So, $$\begin{gathered} d=\left(15.70\right)·\left(140\right) \\ \Rightarrow d=2198 \end{gathered}$$

This means that the athlete travelled approximately $2200m$ in $2$ minutes $20s$.

Find the number of rounds $n$ the athlete completes in $2$ minutes $20s$.

$$\begin{gathered} n=\frac{140}{40} \\ \Rightarrow n=3.5 \end{gathered}$$

since, the athlete completes three and a half rounds in $2$ minutes $20s$.

So, at the end of $2$ minutes $20s$ athlete is on the diametrically opposite side from the starting point.

So, the displacement of the athlete at the end of $2$ minutes $20s$ is $200m$.

Therefore, the distance covered and the displacement at the end of $2$ minutes $20s$ are $2200m,200m$ respectively.

Hence, option $A$ is the correct answer.