Changing the asteroid's velocity changes the time when the asteroid crosses Earth's orbit. After all, just because it crosses Earth's path doesn't mean there is necessarily going to be a collision. It has to cross Earth's path when the Earth is right there.

If we found a hazardous asteroid, we could nudge it out of the way.

NASA has hit a comet with an impactor, during the Deep Impact mission. The goal of that mission was to study the surface by making a crater and stirring up the surface material so it could be studied.

Carrie Nugent Quotes