A particle is moving in a plane with a velocity given by, u→$$=$$ $$u0$$ $$i^$$ $$+$$ $$($$ωa $$cos$$ ω$$t)$$ $$j^$$ , 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 $$t=3$$$$π$$$$2$$ω will $$be-$$

Question

A particle is moving in a plane with a velocity given by,  u→$$=$$ $$u0$$ $$i^$$ $$+$$ $$($$ωa $$cos$$ ω$$t)$$ $$j^$$ , 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 $$t=3$$$$π$$$$2$$ω will $$be-$$

Infinity Learn · Accepted Answer

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 $$t=3$$$$π$$$$2$$ω $$x=u03$$$$π$$$$2$$ω$$---(1)$$  $$uy=$$ $$dydt=$$ωa $$cos$$ ωt $$dy=($$ωa $$cos$$ ω$$t)dt$$ integrating ∫$$dy=$$∫$$($$ωa $$cos$$ ω$$t)dt$$ $$y=wasin$$ ωtω $$y=asin$$ ωt $$y=asin$$ ω$$3$$$$π$$$$2$$ω $$y=-a---(2)$$∴ The displacement of the particle from theorigin is $$x2+y2=3$$$$π$$$$u02$$ω$$2+a2Hence$$ correct answer is (A)

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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-

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