A particle goes along a quadrant from A to B of a circle radius 10m as shown in fig. Find the magnitude of displacement and distance along path shown, and angle between displacement vector `vecAB` and x-axis?

Explanation

Displacement `vec(AB) = vec(OB) - vec(OA) = (10hatj - 10 hati)` m
`" "|vec(AB)| = sqrt(10^(2) + 10^(2)) = 10 sqrt2 `m
From `Delta OBC tantheta = (OA)/(OB) = (10)/(10) =1 rArr theta = 45^(@)`
Angle between displacement vector `vec(OC)` and x-axis = `90^(@) + 45^(@)= 135^(@)`
Distance of path AB = `(1)/(4)` (circumference) = `(1)/(4)(2 pi R) m = (5pi) m`