When I give accelerate? Ford explorer four wheel drive.
what makes the sound of bump and shake while driving down the road on 2005 Ford Explorer
It could be many things, unfortunately and without experiencing the problem first hand or being able to do some basic diagnostic tests its hard to say. It could be exhaust related, a broken exhaust hanger or such, it could be a bad or broken sway bar link or bushing, bad suspension or shock bushings but needs to be check out as it could affect tire wear or safety.