Many highways with steep downhill areas have “run-away truck” inclined paths just off the main roadbed. These paths are designed so that if a vehicle’s braking system gives out, the driver can steer it onto this incline (usually composed of loose gravel or sand). The idea is that the vehicle can then roll up the incline and come permanently and safely to rest with no need of a braking system. In one region of Hawaii the incline distance is 300 m and provides a (constant) deceleration of 2.50 m/s2.
(a) What is the maximum speed that a runaway vehicle can have as it enters the incline?
(b) How long would such a vehicle take to come to rest?
(c) Suppose another vehicle moving faster than the maximum value enters the incline. What speed will it have as it leaves the gravel-filled area?