How to explain force in turning car

[RubinLicht]

Homework Statement

When a car turns or accelerates, you feel and extra force, and some hanging things in the car also shift. How do you explain this phenomena?

Homework Equations

The Attempt at a Solution

My explanation was simply that since the car is a non inertia frame of reference, you experience an imaginary force that pushes you away from the the direction you're turning/accelerating in. You tilt when turning because friction and your new weight exert a torque on your body.
My friend's explanation was that you are "feeling inertia" I do not know how to explain why I think "feeling inertia" is an icky explanation, could anyone explain why this explanation may be right or wrong to me?

My friend and I also had issues with the concept of "feeling an imaginary force"

 

[Biker]

I believe the inertia is right. Remember what Newton said things have a tendency to stay in their state of motion. So if you are going forward you will stay going forward unless something affects you.

When you are in a car and there is a roundabout coming ahead, You will feel a force acting this is fake, it is just a feeling that you want to go in a straight line but friction for example in this situation wants you to have a circular motion in other words to stay with the car. So it will push you to the center but you feel that you are being pushed to outside (Inertia).

Same example with accelerating in a straight line, Your body is at a speed but when you accelerate the car's speed will be faster than yours so you will end up going back but what keeps you from going backward is the chair it pushes you so you get the same accelerating or speed as the car

 

[haruspex]

Seems to me both explanations are saying the same thing. But first, to clarify, it's not the car as a reference frame that matters, it's you as a reference frame.
In your reference frame, you are not accelerating (by definition). But you feel a contact force from the car. We all have an intuitive grasp of Newton's laws, so to explain an unbalanced contact force, yet no acceleration, we invent a mysterious force the other way.