what would cause my car to run fine when it has first started up then after a while first gear will kinda bog down.
main shaft bearing
You could have ignition problems if it is the engine causing the jerk.
A problem in the fuel line could cause it to stall. On a stick shift, letting off the clutch too soon would cause the vehicle to stall.
Bad struts can cause vibrations while coasting in first gear on a 1993 Mitsubishi 3000 GT VR4. A bad tire can also cause this.
A transmission that is sticking would cause a 1997 Plymouth Grand Voyager to die after shifting it into gear. A problem with the ignition system could also cause this.
This is a common problem with these vehicles. The transmission fluid and filter need to be replaced. This is done by dropping the transmission pan.
the rpms should rise and then drop no more then 500 rpms when the fan on the radiator turns on and then off.
Cable too slack.
due to bad cordination between gear and cluch causes this effect
The equipment you would use while playing sports.
An automatic gear would stick in 1st if there is an obstruction. Gears can sometimes break off and cause motion to stop entirely.