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:<math>E_\text{k} =\tfrac{1}{2} mv^2 </math>
A bumper that protects vehicle components from damage at 5 miles per hour must be four times
Until 1959, such rigidity was seen as beneficial to occupant safety among [[Automotive engineering|automotive engineers]].<ref name="Automotive Plastics">{{cite web|title=Physics in the Crumple Zone Demonstrate How Less Stiff Materials, Like Plastic, Can Help Prevent Injury and Save Lives |publisher=Automotive Plastics|url= https://plastics-car.com/Todays-Automobiles/Automotive-Safety/Physics-in-the-Crumple-Zone-2.html |access-date=21 June 2016}}</ref> Modern theories of vehicle [[crashworthiness]] point in the opposite direction, towards vehicles that [[Crumple zone|crumple progressively]].<ref>{{cite web|url= https://www.autoevolution.com/news/how-crumple-zones-work-7112.html |title=How Crumple Zones Work |first=Tudor |last=Raiciu |date=18 October 2017 |website=autoevolution.com |access-date=20 July 2018}}</ref> A completely rigid vehicle might have excellent bumper protection for vehicle components, but would offer poor [[Automobile safety|occupant safety]].<ref>{{cite web |last1=Evans |first1=Leonard |title=11 Occupant protection |year=2004 |url= http://www.scienceservingsociety.com/ts/text/ch11.htm |website=scienceservingsociety.com |quote=The reduction in speed divided by the time over which it takes place defines deceleration. Injury-producing forces are proportional to the deceleration experienced by the occupant. Occupant protection aims at reducing these forces by spreading the occupant's changes in speed over longer times. The theoretical best protection would be for the occupant to slow down from the initial vehicle speed to zero speed at a constant deceleration using the entire distance between the occupant's body and the vehicle's point of impact. In the previous example of an initial speed of 50 km/h, and assuming the driver is seated 2.5 m behind the front bumper, the resulting average deceleration would be 4 G, uncomfortable but unlikely to produce even a minor injury. |access-date=20 July 2018}}</ref>
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