Car isn't running very well

I was looking around and I found a 2000 Hyundai Accent at a dealership, I wasn't able to to test drive (they wouldn't let me shoulda been sign #1) anyways I got it for 1.5k, I knew it needed work but I still got it (wife drives a 1988 Corolla, needs a new car) It has over 90k miles but other than that it looked good.

Anyways she is driving it home and she calls me and tells me the car sucks, so I start driving it. When you floor it in first second (mabye third) it starts jumping really bad, kinda like when you let the clutch out too fast. it also drops off power BAD when you get past 4.5k RPMs it is almost like i hit the brakes. 4th and 5th gear are great though, I can floor it to the redline and I get no problems. Anybody have any ideas what it might be? Spark Plugs? Injectors? I need some help, it isn't very drivable right now and she starts work next week.

I'd diagnose a slipping clutch.

The torque multiplication in the lower gears is most probably the cause of why it doesn't appear in the more direct and overdriven gears (4th and 5th).

A good test is to take the car up a gentle hill and then begin to gently accelerate from a cruising speed. In 3rd gear at 2000 rpm, work out the overall ratio eg 2000 rpm = 40 km/h and then accelerate to 3000 rpm (check that the 3000 = 40 *1.5 = 60 km/h) then to 4000 rpm = 80 km/h and then to 5000 rpm = 100 km/h. If you find that the engine speed is becoming disproportional to the ground speed it's a drive train slippage issue.

two questions -

1) You got the car for $1500?

2) Doesn't it have some ridiculously long warranty on it, to make up for poor quality? (if yes, let the dealer fix it)

Did you do a tune-up on it after you bought it? Replace the plugs & wires, and the cap & rotor... sometimes the distrib cap, plugs, or wires can cause it to jump like that.

I have to agree with the slippign clutch, also with the mild tune up facts. Id replace the plugs, wires, cap, run some injector cleaner threw the gas tank. After that id check out the clutch, you could end up spending more money on the clutch then you did on the car. But other then that I dont konw what to tell you. Hope all goes well.

Would a slipping clutch be a voilent jerking? It's not like a slight loss of power it's like I slam on the brakes.

seen about all of it dont go after ignition it's either comin from the clutch, tranny, or if it's a carb Ive seen them do that just rebuild it to fix it I cant really tell you without lookin at the car have someone who knows what there doin drive it Im in Minnesota so it probably a ways away Good Luck