Why does the car shake when excellerating over 35 most the time but not all the time

Likely a bad axle shaft. If its not had them done already replace front bearings/hubs at the same time if its in the budget. That is if you plan to keep it, but its getting to be an old car. If you're going to sell it soon, as in the next 18 months or so, just drive it. They can vibrate for years without failing. It's annoying at times, but it won't leave you stranded.