Indeed the very concept of temperature of a body is a measure of the amount of motion of the particles that make up a body. Consequences of this can be seen for example if you fill a rubber balloon with air at room temperature. If you now heat the balloon, the size of the balloon will grow. This is not because you are putting more air into the balloon, which you aren't. The balloon grows because the molecules of air are heating up, so the move faster than they did before, so the push harder when they hit the surface of the balloon from the inside, pushing the balloon walls farther out and making the balloon grow in size.
Bigger planets require higher velocities for an object to escape their gravitational pull.
Well actually, it really isn't the size of the planet that matters, but the amount of material, that is, how much mass it has. So this statement is not about big planets, but about massive planets. As we saw when we talked about gravitation and proyectiles and satellites, the more massive a planet is, the stronger the force that it would pull any object with. So it makes sense that it is more difficult to escape the gravitational pull of a more massive planet. On an atmosphere of a given temperature, lighter gas molecules move faster than heavier gas molecules.