Engine mounts needs replacement?

Hi,
When I start my car up in the morning lately, I have a bad vibration noise coming from around the front, passenger side of the car. If I back up, with it when its still "cold" it makes a horrible vibration noise but when put in drive it stops. Sometimes the vibration also sounds like its coming from the middle of the front of my car. It had been in a previous accident before I bought it and I also hit a curb divider well over a year ago because I didn't realize it was in front of my car. Just kind of curious to what it may be. It seems to drive ok and after it warms up for a few minutes, I do not hear the vibration noise again.