Final answer:
Drivers should not operate a vehicle for more than 14 hours after rest due to safety concerns, which is shown in studies like the sleep deprivation experiment on professional drivers, and calculating battery life of headlights involves understanding of physics and mathematics.
Step-by-step explanation:
The question concerning after what elapsed time a driver can not drive relates directly to regulations or guidelines suggesting rest periods for drivers to prevent fatigue. It is generally advised that drivers should not operate a vehicle for more than 14 hours following an off-duty period for safety reasons due to increased risks of accidents after prolonged periods of driving.
Experiment on Sleep Deprivation and Driving
A recent study on sleep deprivation and driving involving 19 professional drivers is an example of an Experimental Design and Ethics topic. The drivers went through two sessions, where their performance was measured post-normal sleep and after 27 hours of no sleep. The randomness of treatment assignment and the use of a driving simulation to measure performance are key factors illustrating the experimental design.
Calculating Headlight Battery Life
The scenario detailing the battery life of headlights left on involves understanding of physics and mathematics. A 12-V automobile battery with a 100 Ah (ampere-hour) rating can theoretically supply a 40 W (watt) headlight for a certain amount of time. By calculating energy consumption, one can estimate the duration the headlights would operate before the battery fully discharges.