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

Explanation

Displacement `vecAB=vecOB-vecOA=10hatj-10hati`
`|vecAB|=sqrt(10^(2)+10^(2))=10sqrt(2)m`
From `DeltaQAB tan theta=(OA)/(OB)=(10)/(10)=1 rArr theta=45^(@)`
Angle between displacement vector `vecAB` and x-axis `=90^(@)C+45^(@)=135^(@)`
Distance of path `AB=(1)/(4)` (circumference) `=(1)/(4)(2piR)m=(5pi)m`