Question

An athlete completes one circle of radius r in 40sec. What will be the displacement at the end of 2min 20 sec.?
A) zero
B) 2R
C) $2\pi R$
D) none

Answer 1

Hint: Find the time taken by the athlete to travel every one fourth of the circle. Next, calculate the given time period in seconds. Check the nearest time at which the athlete returns to initial position. Next, if an athlete travels any extra time, calculate the displacement easily.

Complete answer:
Let us convert the given time into seconds,
$2\min 20\sec =140\sec $
Next, the distance travelled by the athlete for one complete circle will be,
$S=2\pi R$
Now, we were given the time for once circle, let us calculate the number of circles made by the athlete for given time,
$\begin{align}
  & 2\pi R=40\sec \\
 & ?=140\sec \\
 & \Rightarrow ?=7\pi R \\
\end{align}$
Now, the displacement of the athlete will be zero, if we come to the same position where he started initially, that means, he needs to travel a distance which is an integral multiple of $2\pi R$.
The distance travelled by the athlete for a given time is not an integral multiple, therefore, it is not zero.
He travels a distance of $\pi R$ extra,
It means he travels half a circle extra after he reaches initial state.
As displacement is the shortest distance between initial and final positions,
The displacement in this case will be the diameter of the circle.

So, the correct answer is “Option B”.

Additional Information:
Distance is the length travelled by the object in given time. Displacement, whereas, will be the shortest distance between the initial and final positions in given time. The displacement is equal to zero if the object comes back to the initial point no matter wherever it goes during its journey. Same goes in the question, distance would increase eventually, but displacement periodically comes to zero.

Note:
The displacement doesn’t increase with the number of rounds made by the athlete in the circular track. As the rounds made by him increases, he crosses his initial point periodically, making the displacement start from zero again. Therefore, the displacement is a lot different from distance in physics.