A toy race car starts from rest on a circular track of radius 4.30 m. The cars speed increases at the constant rate of 2.90 m/s2. At the point where the magnitudes of the centripetal and tangential accelerations are equal, determine (a) the speed of the race car.

Answer 1

R=4.3 m, a(τ)=8.8 m/s²
a(τ)=a(c) =v²/R =>
v=sqrt{a(c) •R}= sqrt{a(τ) •R}=
=sqrt{8.8•4.3}=6.15 m/s
v=a(τ) •t,
t= v/a(τ)=6.15/8.8 =0.699 s= 0.7 s.
s= a(τ) •t²/2 =8.8•0.7²/2=2.156 m.