Circular motion vector problem

[devanlevin]

a particle starts its movement in a cirlce (R=2m) with tangential acceleration aT(t)=0.004t. if at the start of the motion, the particle's palcement vector (r) was pointing straight down, and the particle is moving clockwise fins



a) how long will it take till the angle between the vector of velocity(V) and the vector of acceleration is equal to 60 degrees?



b) what distance will the particle cover in this time?



c) what is the angle of the placement vector at this time?

 

[devanlevin]

what i did was the following:
aT=0.004t
v=integralaT=0.002t^2

aN=v^2/r=2*(10^-6)t^4

now i know that aN perpendicular V
and that aT parallel to V

so i built a triangle made up of the vectors aT and aN - ie the vector components of a.
now the angle between a and aT, alpha, is equal to the angle between a and V, so
tg(alpha)=aN/aT
i want to know when alpha=60
tg60=sqrt3= 2*(10^-6)t^4/0.004t
t=15.13s

is this correct