Seems if it goes that fast, then all the target has to do is cut power as soon as it senses the approach, and the missile will probably overshoot. Power cut would be near instantaneous. I doubt anything that fast can make a very tight turn.
Filed under "famous last words."
Seems like, at that speed, wouldn’t matter if the target ‘cuts power’. As you mentioned, the weapon is moving so fast that it is doubtful it would even have time to ‘change course’ enough to miss the target.
That is assuming the target is moving in the first place.
At 5x (3500mph) the closing speed would be so fast if it was a vehicle it would need some good brakes, a ship couldn’t alter course fast enough.
google losat videos and watch what happens as losats close in on moving targets.