The science and math in TPS is sloppy as hell. An asteroid doesn't travel all that fast astronomically speaking. Compared to a starship it's practically crawling along. If it took an extended period of time (say hours) to reach the asteroid at Warp 9 then that sucker was really far away and likely out past the outer reaches of the solar system. In other words they had a lot of freakin' time before it reached the planet.
If the asteroid were only a couple of months away from the planet then the Enterprise could reach it in seconds at Warp 9.
Even crippled if the Enterprise can manage a tenth of light or .1c on impulse then they'd still outrace the asteroid by hundreds to thousands of times the asteroid's speed.
If the asteroid were only a couple of months away from the planet then the Enterprise could reach it in seconds at Warp 9.
Even crippled if the Enterprise can manage a tenth of light or .1c on impulse then they'd still outrace the asteroid by hundreds to thousands of times the asteroid's speed.