Car Passing Maneuver Safety Analysis · CAP 2002 #B1
Physics · mechanics
Problem
Passing a car on a two-lane road requires more caution as speeds increase. Apart from maintaining a safe distance between vehicles in the same lane, there should also be enough space between oncoming vehicles while the passing manœuvre takes place.
Take all cars initially, travelling at the same constant speed, to have a length 4.2 m. Suppose further that a passing manœuvre starts with the passing car at least 3.0 car lengths behind the back of the slower car, and that it ends when the driver has pulled in with the back of her car at least 3.0 car lengths ahead of the slower car (no fish-tailing!). The passing car takes 4.0 s at constant acceleration to reach its final passing speed, which it keeps thereafter. This final speed is 11 km/hr greater than the steady speed of the slower car.
(a) Calculate the total time it takes for such a passing manœuvre.
(b) Now suppose that at the instant the passing driver has reached her overtaking speed, she notices 500 m ahead (from the front of her car) a very large truck coming toward her. The speed limit for trucks on that road, which we shall assume the truck driver respects, is 90 km/hr. The slower car is driving at 100 km/hr. Otherwise, the same conditions as in part (a) apply. We assume that for minimal safety she should have completed her manœuvre at least 2.0 s before the truck and her pass each other, But she cannot abort the manoeuvre without braking unless the front of her car is at least 2.0 m behind the back of the slow car, and she cannot brake safely because another car right behind her is also trying to pass the slow car. Given that it takes her 1.6 s to react after she first sees the truck, discuss whether it is safe for her to continue, or whether she should pull back behind the slower car (if she can!). If it turns out that she is in trouble, could she continue accelerating at the same rate up to a higher speed not exceeding 120 km/hr and pass safely while still pulling in three car lengths in front of the slow car?