Tangential acceleration of a particle moving in a circle of radius 1 m varies with time t as shown in figure (initial velocity of the particle is zero). Time after which total acceleration of particle makes an angle of 30 ° with radial acceleration is

Step-by-step solution

Given that a t t = tan 60 o ⇒   a t = 3 t             … 1 dv dt = 3 t ⇒     ∫ 0 v dv = 3 t dt v = 3 t 2 2 ...(2) Given that tan 30 o = a t a c             ⇒   1 3 = a t a c   ⇒  a c = 3 a t v 2 R = 3 a t             … 3 From (1) and (2) 3 2 t 2 2 1 = 3