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Q.

A particle moves in xy plane. The position vector at any time / is r→=(2t)i^+2t2j^m. The rate of change of θ at time t = 2 second (where θ is the angle which its velocity vector makes with positive x-axis) is

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a

217rad/s

b

114rad/s

c

47rad/s

d

65rad/s

answer is A.

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Detailed Solution

x=2t⇒vx=dxdt=2Y=2t2⇒vy=dydt=4ttan⁡θ=vyvx=4t2=2t∴Differentiating with respect to time we get,sec2⁡θdθ2=2or 1+tan2⁡θdθ2=2; or 1+4t2dθdt=2or dθdt=21+4t2;dθdt at t=2 is dθdt=21+4(2)2=217rad/s

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A particle moves in xy plane. The position vector at any time / is r→=(2t)i^+2t2j^m. The rate of change of θ at time t = 2 second (where θ is the angle which its velocity vector makes with positive x-axis) is