To get a feeling for inertial forces discuss the familiar cases of accelerating in a car in a straight line while increasing or
decreasing speed and turning the wheel to change direction. What direction do you feel a force in these scenarios and how does the strength of that force change if you either hit gas/brake harder or turn sharper?
When we accelerate in a car on a straight path we tend to lean backward because our lower body part which is directly in contact with the seat of the car gets accelerated along with it but the upper the upper body experiences this force later on due to its own inertia. This force is accordance with Newton's second law of motion and is proportional to the rate of change of momentum of the upper body part.
Conversely we lean forward while the speed decreases and the same phenomenon happens in the opposite direction.
While changing direction in car the upper body remains in its position due to inertia but the lower body being firmly in contact with the car gets along in the direction of the car, seems that it makes the upper body lean in the opposite direction of the turn.
On abrupt change in the state of motion the force experienced is also intense in accordance with the Newton's second law of motion.
