Reason behind Inertia Has any physicist work on the reason behind Inertia?
Why do we have inertia only during acceleration?
No inertia during constant velocity.
 A: You have inertia all the time. Physics has advanced since Newton.
Now we know that an object has energy and momentum and that they combine together to give a 4d energy-momentum vector with four components. And mass is the length of that vector.
When objects have relative velocities that are small compared to the speed of light, those vectors point in almost the same direction so the sum of the lengths is really close to the length of the sum. And that's why two bowling balls have a mass that is really close to the sum of the mass of each.
We've also learned that mass isn't the source of gravity, that the stress-energy tensor is and that empty space itself can be curved in its own, even far from stress-energy.
We've also learned that you don't have to have mass to be affected by gravity.
And we learned that forces are really about exchanges of energy and momentum and so you can experience a force by exchanging energy and momentum with a field, even a field with zero mass (and that the squared lengths of the energy momentum can be zero even when the vector is nonzero).
So we've learned a lot.
A: Look inertia is present all the time. But you can feel it only when your state of rest or motion is changed because of acceleration. This doesn't mean that you have inertia only during acceleration.
Inertia is just a property due to which we remain at the same place as mentioned by Timaeus . 
When you are standing on a bus and the bus accelerates then your feet accelerates with the bus due to friction but there is no force on your upper part and so it remains at its position ( due to inertia) . This is the reason why you feel inertia while accelerating.
