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## Homework Statement

A car is driven along straight section of track length (r). The car started from rest and the time it took to cover r distance is (t). If the same car is then tested on a circular arc of radius r, starting from rest and continues to speed up at the maximum possible rate that allows it to remain on the track, how long would it take to traverse the arc?

## Homework Equations

V_avg = (V_f + V_0) / (2)

V_avg = r / t

a = (V_f - V_0) / t

a =V^2 / r

## The Attempt at a Solution

V_0 = 0

V_avg = (V_f) / 2. V_f = 2 * V_avg

a = (2 * r) / t^2

a = (v^2) / r = (2 * r) / t^2

t^2 = (2 * r^2) / v^2

t = (r/v) * sqrt(2)

That is what I got for time, I think I'm doing it correctly, but my classmates have different answers for the time it took to traverse the arc. Is there an error in my work?

Thanks :)

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