Vibrating/grinding sound upon acceleration

[Shawn5800]

Hey guys, i have had my 98 Prizm for about a year now, and since i bought it, till now (24,000 miles later) It has had this stupidly annoying vibrating or grinding sound upon first acceleration. I notice that it does it the most starting on a hill and with a heavy load in the vehicle, or if i really get on the gas from a stop it makes a horrible grinding sound right under the passenger floorboard and goes away as soon as the car is up over 10 mph about. It almost sounds like when you drive over those drifting warning bumps on the highway except not as intense.

I cant figure out for the life of me what this could be. I have had the car on a lift while doing a tire rotation, etc and couldnt see anything broken or out of ordinary. It really scares me to get on the pedal sometimes because im not sure if its really bad... I just want it fixed so i can have nice quiet smooth acceleration.

Otherwise, i bought my car for $500 and 24k miles later in less than a year i have only had to do fluids and a serpentine belt. And wheel balance. She now has 185k on her. This car is amazing. I will keep it until it dies. Props to Toyota for a rock solid car.