After a while you decide you don't want to go any faster, so you stop accelerating, and your speed stays the same. BUT you accelerate again because you are changing directions. The first grader you are pulling feels the acceleration, and has to hold tightly on to the sides of the wagon to keep from falling out. If you decide to slow down, you would also be accelerating, but most people call it deceleration to distinguish between speeding up and slowing down. All mass pulls on all other masses with gravity.
Gravity is VERY weak though.
In fact, gravity is so weak that it take a HUGE amount of mass for its effects to be noticeable. You have mass, and therefore, you pull other masses toward you with your gravity. It doesn't matter how far away something is, your gravity is still pulling on it. The pull of your gravity on an object does get weaker the farther away from you another object is. It doesn't matter, though.