question about supernova kinetic energy

lr1

A9: Supernova Remnants
Consider a supernova explosion in the outer 4M⊙ of a dying star, ejected at a speed of 5000 km/s.
a ◮ What is the kinetic energy of the expanding ejecta?
b ◮ The ejecta are slowed by sweeping up the local interstellar gas. Assuming the density of the interstellar gas
is ig = 2 × 10−19 kg/m3, how large a volume will be swept up by the time the outflow velocity has decreased
to 10 km/s? HINT: Assume the KE of the expansion is conserved.
A10:

tiny-tim

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lr1

Part a I used virial theorem for kinetic energy 3mv^2 and for part b I used mass= density / volume but am confused with swept volume

Chronos

Virial theorem is only useful on large scales, for a region near a supernova event you still need to use kinematical models.