On an otherwise straight stretch of road near Moffat, Colorado, the road suddenly turns. This bend in the road is a segment of a circle with radius \(110 \mathrm{~m}\). Drivers are cautioned to slow down to \(40 \mathrm{mph}\) as they navigate the curve.

a. If you heed the sign and slow to \(40 \mathrm{mph}\), what will be your acceleration going around the curve at this constant speed? Give your answer in \(\mathrm{m} / \mathrm{s}^{2}\) and in units of \(g\).

b. At what speed would your acceleration be double that at the recommended speed?