Question

At t = 0 particle starts and moves in a circular path of radius r if tangential acceleration of the particle is 'a' then find the time when the total acceleration vector makes an angle 45 with tangential acceleration vector?
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Answer 1

tangential accln at = dv/dt = a. (given)

radial accln ar = v²/r

Since resultant accln makes angle 45° with at

tan45° = (v²/r)/(dv/dt)

∴ v²/r = dv/dt

dt = v² dv/r

∫dt = ∫v² dv/r between limits t = 0 and t= t

t = v³/3r

= ( v²/r) xv/3

= av/3