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

Step-by-step solution

x = 2 t   ⇒ v x = d x d t = 2 y = 2 t 2   ⇒ v y = d y d t = 4 t ∴   tan ⁡ θ = v y v x =   4 t 2 = 2 t Differentiating with respect to time we get, sec 2 ⁡ θ   d θ d t = 2 or 1 +   tan 2 ⁡ θ   d θ d t = 2 or 1 + 4 t 2   d θ d t = 2 or d θ d t = 2 1 + 4 t 2   d θ d t a t   t = 2   s   i s   d θ d t = 2 1 + 4 2 2 = 2 17   r a d   s - 1