Question

A particle moves over three quarters of a circle of radius ‘r’. What is the magnitude of its displacement?

Answer 1

r'=r √2 
this will be the value of displacement 

Answer 2

A particle moves over three quarters of a circle of radius r. What is the magnitude of its  displacement?

Radius of circle =r

Body moves over 3 quarters

Magnitude of displacement = the hypotenuse of the 4th quarter whose Base and perpendicular r both = r unit.

Then,

(Hypotenuse)² = base² +perpendicular²

H² =r² +r²

H^2=2r²  

H=√2r²

The magnitude of its displacement √2r²