In the novel, Wade's DeLorean contains a plutonium chamber that is rigged to explode if another avatar tries to steal the car. How feasible are nuclear-powered cars in our world?

Nuclear-powered cars are an exciting concept! At present, environmentally friendly nuclear-powered submarines and aircraft carriers are already a reality. The benefits of nuclear energy include its formidable energy density, its clean-burning efficiency, and its long-lasting power. Ford premiered the Nucleon and the Ford Seattle-ite XXI in 1958 and 1962 respectively; both were nuclear-powered vehicle prototypes. Unfortunately, the cars were never mass-produced.
Engineers were unable to create automobile-sized nuclear reactors that could facilitate the atomic fission needed for combustion. At present, small-scale nuclear reactors remain a design challenge. Additionally, because uranium is radioactive, the massive layers of shielding needed to protect passengers were considered prohibitive to vehicle propulsion. Modern engineers are working on using thorium in automobile engines, however, which is far less radioactive than uranium. So, while nuclear-powered cars remain in the realm of science fiction, the possibilities for nuclear power are endless. Fortunately, a thermonuclear blast caused by Wade's DeLorean will kill only avatars, not actual humans!