What is the breaking distance $($ ft $.)$ for a vehicle from an initial speed $55$ mph to a final speed of $35$ mph $?$ Assume the coefficient of friction is $0\mathrm{.}5$ and $5\%$ downgrade.

A$.144\mathrm{.}2$

B$.134\mathrm{.}2$

C$.154\mathrm{.}2$

D$.164\mathrm{.}2$