Question

Calculate the distance and displacement of a body after completing ¾ part of the circular path.

Answer 1

Answer:

The distance covered

$= 2\pi \times r \times \alpha \div 360 \\ = 2\pi \times r \times 270 \ \div 360 \\ = 2\pi \times r \times 3 \div 4$

displacement is

$s ^{2} = r {}^{2} + r {}^{2} \\ s {}^{2} =2 \times r {}^{2} \\ s = \sqrt{2 \times r ^{2} }$

Answer 2

Answer:

Let, radius of the circular path = r units.

(3 / 4)th of the circular path = traversing through an angle 270°.

Distance travelled = (3 / 4) * (2 * π * r) units = (1.5 * π * r) units.

Remaining angle to cover one complete round = (360° - 270°) = 90°.

Displacement = {2 * r * sin (90° / 2)} units = {(√2) * r} units at an angle 45° backward.