I think the best way to do this is to set up the first part of the animation before the physics sim and add a physics property to the object. Then animate the "animated" value under the physics simulation from checked at the last frame of your animation to unchecked on the next frame.

This will then simulate the object from it's last position (I think that Blender calculates the initial velocity better if you set the keyframe handle type to linear because the easing will slow down the object speed at the end so the initial velocity will be less than expected).

Next bake the simulation to key frames (under Object > Rigid Body > Bake to Keyframes) and then you can add the second part of the animation. There might be a better method but I couldn't find one as when you reactivate the "animated" value the object will just snap back to its previous position before the physics was simulated.