**A race car starts from rest on a circular track of radius 493 m. The car speeds up the rat constant?**

*A race car starts* from rest on a circular track of radius 493 m. The car's speed increases at a constant rate of 0.650 m/s2. At the point where the magnitudes of the centripetal acceleration and tangential directions are equal, find the (a) speed racing car (b) the distance traveled (c) time

the linear velocity at any time t is v (t) = v0 + at = 0 0.65 t the radial acceleration is v ^ 2 / r = (0.65t) ^ 2 / r is the tangential acceleration 0.65m/s/s, which are equal when: 0.65 = (0.65t) ^ 2 / 493 or t = sqrt [493 / 0.65] = 27.5s when t = 27.5 s, the linear velocity is 27.5 0.65m/s/sx s = 17.9m / s , the distance covered at this time is dist = v0t +1 / 2at ^ 2 = 0 +1 / 2 (0.65m / s / s) (27.5s) ^ 2 = 245.8m (note: previous solution ignores the factor of 2 in the equation: vf ^ 2 = v0 ^ 2 +2 ad d = 2/2a vf ^ ^ 2/1.3 = 9.17 = 246M)

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