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R = acos@ (i) + asin@ (j) ................1
R is the position vector of particle at any time performing circular motion...
@ is angular displacement
w = @/t
@ = wt ..............2
from 1 & 2
Rt = acoswt (i) + asinwt (j) .............3
at t = 0 ,
Ro = a (i) ..............4
displacement = Rt - Ro = a(coswt-1) (i) + a(sinwt) (j)
magnitude =[ (a2(coswt-1)2 + a2(sinwt)2]1/2
= [2a2 - 2a2coswt]1/2
= a[2(1-coswt)]1/2
now , coswt = (1-2cos2(wt/2)) , after putting this in above eq
magnitude = 2a[cos2(wt/2)]1/2
=2acos(wt/2)
this is the required result ,
approve if u like my ans
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