It depends because some missiles don’t hit targets while the rocket engine is running. Often the rocket engine sends the rocket into a parabolic trajectory and shuts off at the peak altitude and then it coasts to the target while moving to avoid AA. HIMARS does that but there are missiles that don’t, but they aren’t labelled hypersonic like the javelin.
The idea behind hypersonic is that’s it’s always at hypersonic speeds which means very hard to intercept. Half hypersonic is how many missles works.