Why does your body feel like it is being pushed back when the car starts back up again?

Answer 1

That is the result of Newton's 3rd law of motion, which is inertia. Your body wants to remain at rest as the car accelerates, and the car has to push on you to get you moving. This is why you feel like you're actually being pushed forward, unless you're accelerating backward. It is the exact same reason you tend to lean while cornering, as well. Also, when you brake, this is why you tend to feel like you're being pulled foreword.

Inertia is the tendency for things at rest to stay at rest until an outside force acts upon it. Also, a body in motion tends to want to stay in motion (in a straight line) until an outside force acts upon it to change it.