A particle is moving in a plane with a velocity given by,  u→= u0 i^ + (ωa cos ωt) j^ , where i^ and  j^ are unit vectors along x and y-axes respectively. If the particle is at the origin at t = 0, then its displacement from the origin at time t=3π2ω will be-

Let uX and uy be the components of the velocity of the particle along thex- and y-directions. Thenux= dxdt= u0   x=u0t   ; substitute given value of t=3π2ω x=u03π2ω---(1)  uy= dydt=ωa cos ωt dy=(ωa cos ωt)dt integrating ∫dy=∫(ωa cos ωt)dt y=wasin ωtω y=asin ωt y=asin ω3π2ω y=-a---(2)∴ The displacement of the particle from theorigin is x2+y2=3πu02ω2+a2Hence correct answer is (A)