How do rockets prevent rear-ending after stage seperation?

Question

On the third flight of SpaceX's Falcon 1, the following failure occurred according to one narrative.

We turned off the first-stage engine and then proceeded to separate the vehicle stages; however, when the stages uncoupled, there was still a little leftover "kick," or thrust, in the first-stage engine. Our first stage literally rear-ended our second stage immediately after we had tried to separate the two sections of the vehicle. It was a devastating, emotional experience.

Sounds logical. You wouldn't want to wait until your prior stage fully putters out completely before separating because (among other things) you'll lose altitude. Ideally, you'd want to be delivering as much thrust as possible as constantly as possible, and that might entail having some kick left in the prior stage.

In the general sense (not specific to SpaceX), how is this avoided in vertically staged rockets?

Answer 1

This type of failure is known as separation failure which is caused due to timing error in separating the stages

Musk said SpaceX would be releasing video of the staging event that clearly shows that the first and second stages separated as planned about 2 minutes and 20 seconds into the flight, but that unanticipated residual thrust from the redesigned Merlin engine caused the first stage to bump the second stage just as it began to fire

This is normally overcome in the rockets by

• shutting down the rocket engine properly (cutting down the fuel source(liquid propellent) in case of solid propellent it is impossible to shut down so timing is very important the fuel is entirely burnt before shut down)

Source:

The separation of large boosters uses direct staging. Each booster is connected to the rocket’s core through a bar mechanism in the front joint side and the round head mechanism in the back joint side. When the engine of the booster stops working, the connection bolt and separation nut will be unlocked separately. The small separation rockets that are bound to the boosters are ignited and separate the boosters from the core. The boosters fall down and separation is complete.