Each Car has Speed Corresponding to Max Normal Acceleration. Find Time Elasped

[Northbysouth]

Homework Statement

The two cars A and B enter an unbanked and level turn. They cross line C-C simultaneously, and each car has the speed corresponding to a maximum normal acceleration of 0.94g in the turn. Determine the elapsed time for each car between its two crossings of line C-C. What is the relative position of the two cars as the second car exits the turn? Assume no speed changes throughout.

I have attached an image of the question.

Homework Equations

a_n = v²/ρ = rθ'² = vθ'

v = rθ'

The Attempt at a Solution

I' honestly not sure how to start this one. I know a_n = 0.94g = 9.2214 m/s²

I was thinking of something along the lines:

v = rθ' = r dθ/dt

∫v dt = ∫r dθ

vt = rθ

t = rθ/v

I'm not sure if what I have here makes sense. But if it does, could I substitute v for ds/dt, where ds/dt would be the circumference of the half circle?

Honestly,I'm not sure if what I have makes sense. Any input/feedback would be greatly appreciated.

 

[LawrenceC]

Determine the speed of each vehicle from the formula V^2/r=a. Knowing the speed of each, determine the elapsed time for each vehicle to travel the distance realizing the distances differ. Then determine distance between vehicles.