A car starts from rest on a curve with a radius of 100m and accelerates at 1.0m/s^2 .Through what angle will the car have traveled when the magnitude of its total acceleration is 2.1m/s^2 ?
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Expert's answer
2012-10-17T09:53:54-0400
Angle (in radians) X = (2 * Pi) * L / (2 * Pi * R) = L / R Total acceleration at = a + V^2 / R V = sqrt( (at - a) * R ) t = a / V = a / sqrt( (at - a) * R ) X = L / R = (a * t^2 / 2) / R = (a * (a / sqrt( (at - a) * R ))^2 / 2) / R = (a * (a^2 / ( (at - a) * R ) / 2) / R = (a^3 / ( 2 * (at - a) * R^2 )) = 1^3 / ( 2 * 1.1 * 100^2 ) = 1 / 22000 Answer: 1 / 22000 radians.
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