The Fourth Amendment prohibits unreasonable searches and seizures. Police use of force to stop someone constitutes a seizure. So, when the police use force—for example, to end a high-speed car chase—the question is whether they did so reasonably.
The Supreme Court & Car Chases
In Plumhoff v. Rickard, the Supreme Court found that police officers acted reasonably in shooting 15 times at and killing a man trying to escape by car. (572 U. S. ____ (2014); the officers also killed the man’s passenger—the Court didn’t decide whether they violated her Fourth Amendment rights.)
The driver in Plumhoff had taken several officers on a chase that lasted over five minutes, exceeded speeds of 100 miles per hour, and affected other cars on the road. When the man was temporarily cornered in a parking lot, he continued to try to escape. An officer fired three bullets into his car at close range. After the driver freed his vehicle and began to speed away, officers fired 12 more shots. The car crashed into a building; both the driver and passenger died of a combination of gunshot wounds and collision injuries.
The Supreme Court said that it wouldn’t consider police action in these kinds of cases “with the 20/20 vision of hindsight.” It repeated a previous holding that police attempts to end high-speed chases that threaten innocent bystanders’ lives don't violate the Fourth Amendment. It then held, “[I]f police officers are justified in firing at a suspect in order to end a severe threat to public safety, the officers need not stop shooting until the threat has ended.”
The Court issued a similar ruling in 2015's Mullenix v. Luna. In that case, the Court found that a Texas officer was immune from a lawsuit for killing a fleeing suspect. The suspect had been trying to escape via car at high speeds on the highway and had threatened officers by phone while driving; the officer shot at the suspect's car several times.
Talk to a Lawyer
If you want to know whether the police used legally excessive force against you or a family member, consult an experienced lawyer in your area. The law can vary from state to state, from state to federal court, and even between courts in the same jurisdiction, such that only a knowledgeable attorney can properly advise you of the law.