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?
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?
Step 1: Given that:
The radius of the circular track = R
Time(t) to complete one round of circular track by athlete = 40sec
Total given time(T) = 2min20sec = 2×60sec+20sec=140sec
Step 2: Calculation of the magnitude of displacement :
Displacement = Shortest distance between the initial and final point of the path
In the circular path, for one complete round, the initial and final point is the same.
Hence,
Displacement in one complete round of circular track = 0
Number of complete turns(n) in the given time = Totaltimetimetakentocompleteoneround
Therefore; n=140sec40sec=3.5
In half round the shortest path = diameter of the circular path
Thus, the total displacement of the athlete = Total displacement in three complete rounds + displacement in 0.5 round
= 0 + diameter of the circular track
= 2R
Thus,
Option C) 2R is the correct option.
Step 1: Given that:
The radius of the circular track = R
Time(t) to complete one round of circular track by athlete = 40sec
Total given time(T) = 2min20sec = 2×60sec+20sec=140sec
Step 2: Calculation of the magnitude of displacement :
Displacement = Shortest distance between the initial and final point of the path
In the circular path, for one complete round, the initial and final point is the same.
Hence,
Displacement in one complete round of circular track = 0
Number of complete turns(n) in the given time = Totaltimetimetakentocompleteoneround
Therefore; n=140sec40sec=3.5
In half round the shortest path = diameter of the circular path
Thus, the total displacement of the athlete = Total displacement in three complete rounds + displacement in 0.5 round
= 0 + diameter of the circular track
= 2R
Thus,
Option C) 2R is the correct option.
