Help with implicit differentiation/related rates. Which car is turning faster?

[KrabLord]

In particular, I am curious as to how the velocities are implemented in the problem. Help with finding the solution would be appreciated.

 

[Dr.Peterson]

Is there any context to make it clearer exactly what they mean by "turn faster"? Any instructions for this set of problems that explain their setting, or any preceding problem that sets it up? I assume "your radius" means the radius of the circle on which you are driving, and "further out" refers to a circle farther from the same center.

My first thought is to calculate the rate of turn in radians per second in each case, and compare. I see no need to use calculus, but this could be a lead-in to other problems that would call for it.

 

[MarkFL]

Linear speed \(v\) and angular speed \(\omega\) are related by:

[MATH]v=r\omega[/MATH]
where \(r\) is the radius of the motion. Thus:

[MATH]\omega=\frac{v}{r}[/MATH]
Can you proceed?