I would think the only way ATC radar could determine the speed of debris is if the debris is moving directly towards or away from the radar, and it monitored the Doppler shift of the radar return, and even then only if the explosion occurred immediately before the radar painted the target.
I wouldn’t think ATC radars would do speed determination via doppler shift; that would only show speed relative to the radar station. Speed would be actually determined by a dx/dt calculation.
Very good explanation.
dx/dt would require painting the target again on the next rotation of the antenna. By then drag has slowed the debris.
Since most ATC primary radars have a 6 second internal, they wouldn’t be very helpful for something that far off the coast.