A car is traveling up a 2% grade at 70 mi/h on good, wet pavement. The driver brakes to try to avoid hitting stopped traffic that is 250 ft ahead. The driver's reaction time is 0.5 s. At first, when the driver applies the brakes, a software flaw causes the anti-lock braking system to fail (brakes work in non-anti-lock mode with 80% efficiency), leaving 80 ft skid marks.
After the 80 ft skid, the anti-lock brakes work with 100% efficiency.
How fast will the driver be going when the stopped traffic is hit if the coefficient of rolling resistance is constant at 0.013? (assume minimum theoretical stopping distance and ignore aerodynamic resistance)