Roadkill is an almost unavoidable aspect of modern vehicles and roads. It is estimated that over 250,000 animals are killed by automobiles every year in the United States. Most of these accidents are unintentional and can be dangerous.
However, experiments using fake, rubber animals placed on the edge of the road, have found that a small percentage of drivers will attempt to deliberately hit them. Up to 6% of drivers will do this when they see an animal like a tarantula, but slightly more than 2% will attempt to hit even seemingly harmless animals, like turtles. About 3% of drivers in one experiment stopped and attempted to rescue the animal.
As well as being dangerous behavior, road accidents can have a detrimental effect on already vulnerable wildlife populations.
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I'd never swerve and risk myself to save a dog or a cat.