Question

4- Imagine the situation which a vehicle pulls out onto a single-lane highway that has a flow rate of 400 veh/h (Poisson distributed). The driver of the vehicle does not look for oncoming traffic. Road conditions and vehicle speeds on the highway are such that it takes 2.2 seconds for an oncoming vehicle to stop once the brakes are applied. Assuming a standard driver reaction time of 2.5 seconds, a) (8%) what is the probability that the vehicle pulling out will get in an accident with oncoming traffic? b) (10%) What should be the reaction and braking times of oncoming vehicles so that the probability of an accident is equal to 0.25?

Answer 1

sol üts the vehicle beadways between successive Venicles are greater then (2-5 +2.2) = 4.7 sec the driving pull out will not be an accident so, the headways are less then 4.7 sec The deiver pulling - - out will be is a an accident t=4.7 See q = 400 venin Then 1 = 0.0111 Venisec. Pr(hay.7) = 1-elt 0.111x 4.7 El- e 31-6.5932 Prche4-7) = 0.4667 b 40.671. probalility that whide publing out will get an accident 40-474 Given Pr (hat) = 0.25 cat Pr chat) I-e - 0-xt 0.25= i-e t = 2.589 sec reaction time is 2.5 sec. 2.589-2-5 Breaking time is 0.089 sec GS Scanned Breaking time is = 0.089 sec CamScalzer