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Question

# The position vector of a moving particle in x−y plane can be represented as →r=(2tˆi+2t2ˆj)m, where t represents the time instant. The rate of change of θ at time t=2s. (where θ is the angle which its velocity vector makes with positive x−axis)

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Solution

## The correct option is B 217 rad/sHere the position vector is shown in the diagram below x=2t⇒vx=dxdt=2y=2t2⇒vy=dydt=4t ∴ tan(θ)=vyvx=4t2=2t Diffrentiating with respect to time we get, (sec2θ)dθdt=2 or (1+tan2(θ))dθdt=2, or (1+4t2)dθdt=2 ∴ dθdt=21+4(2)2=217 rad/s For detailed solution watch the next video.

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