A race car starts from rest on a circular track of radius 500 m. The car's speed increases at the constant rate of 0.520 m/s2. At the point where the magnitudes of the centripetal and tangential accelerations are equal, find the following.

Question

A race car starts from rest on a circular track of radius 500 m. The car's speed increases at the constant rate of 0.520 m/s2. At the point where the magnitudes of the centripetal and tangential accelerations are equal, find the following. 
a)speed of the race car (m/s)
b)the distance traveled (m)
c)elapsed time (s)

The answer that is on the other questions asked is wrong...please help!

Elena · Answer

a(τ)=0.52 m/s², R=500 m
v=? s=? t=?
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v=a(τ) •t
centripetal (normal) acceleration is
a(n)=v²/R =( a(τ) •t)²/R = a(τ),
a(τ) ² •t²/R = a(τ),
t=sqrt{R/a(τ)}=sqrt{500/0.52)= 31 s,
s=a(τ) •t²/2 = 0.52•31²/2 =249.9 m,
v= a(τ) •t =0.52•31 = 16.12 m/s.