Brake Problem and excellerate on 2005 Mercury Montego

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We need to know what is the problem when you step on the brakes the is a thumping and dragging,the car feels as it is going over horizontal grooves. The front brakes were just ground down and the rear was checked. They claim nothing is wrong but it should stop smoothly. Next problem, when you step on the gas it makes a loud clunk when it goes to the next gear.The car is serviced and checked throughout the year and every time it goes in for an oil change, rotate the tire something major happens. What do we have to look forward to on getting these problems fixed
(1) Answer
Have the CV Shafts checked as strange noises and vibrations happen with worn out CV Shafts and you can find a shop here and check prices here