An Athlete completes one round of a circular track of radius R in 40 sec. What will be the magnitude of displacement at the end of 2 min 20 sec?

The magnitude of displacement at the end of 2 min 20 sec will be 2R

Displacement

The term “displacement” refers to a shift in an object’s position. It is a vector quantity with a magnitude and direction. The symbol for it is an arrow pointing from the initial location to the ending place.

Step 1: Given that the radius of the circular track = R

Athlete’s time (t) required to finish one lap of a circular track = 40 sec

Total given time(T) = 2 min 20 sec = 2 x 60 sec + 20 sec = 140 sec

Step 2: now we have to calculate of the magnitude of displacement:

Displacement = Shortest distance between the initial and final point of the path

The starting point and ending point of the circular path are identical for one full rotation.

Hence,

Displacement on a circular track equals zero after one full turn.

Number of complete turns(n) in the given time = Total time/ Time taken to complete one round

Therefore n = 140sec/ 40 sec = 3.5

The diameter of the circular path is equal to the half-shortest round’s path.

The athlete’s overall displacement is calculated as follows: Total displacement in three full rounds + displacement in 0.5 rounds.

= 0 + diameter of the circular track

= 2R

Hence, Option C) 2R is the correct option.