A certain truck can slow at a maximum rate of 4.6 m/s2 in an emergency. When traveling in this truck at a constant speed of 19 m/s the driver spots a large hole in the road 48.2 m in from of his position. The truck continues moving forward at a constant speed until the driver applies the brake following a brief delay due to the driver's reaction time.
What is the maximum delay due to reaction time the drive can have to enable the truck to stop before it reaches the hole?
Solve for t to find the breaking time.
0 = 19m/s - t_b 4.6m/s^2
Substitute to find the breaking distance.
d = t_b 19m/s - t_b^2 2.3m/s^2
Find the time to travel to that point.
t_d = (48.2m - d) / 19m/s.