Question

An athlete completes one round of a circular track of radius R in 20 s. Her displacement at the end of 2 min 20 seconds is - 

1. 28πR
2. 12πR
3. πR/6
4. zero

Answer 1

Correct Answer - Option 4 : zero

The correct answer is option 4) i.e. zero

CONCEPT:

• Distance refers to the total path covered by an object during its motion or during a time interval.
  • The SI unit of distance is meter (m).
  • It is a scalar quantity and thus, has only magnitude.
• Displacement is the distance between the initial and final position after the motion or journey of an object.
  • Displacement is a vector quantity and can be obtained from the difference of position coordinates of the initial and final positions.

CALCULATION:

Distance covered by the athlete in one round, D = 2πR

Time taken for one round, t = 20 s

Speed of the athlete, s = D/t = 2πR/20

Distance covered in 2 min 20s i.e. 140 s will be = s × time = \(\frac{2\pi R}{20} \times 140 = 14\pi R\)

Number of rounds completed in 140 s = \(\frac{14\pi R}{2\pi R} = 7\)

• As the athlete completes 7 complete rounds, she will be at the starting point once again.
• Hence, displacement is zero.