Velocity is speed (magnitude) plus a direction (vector)
Acceleration is a change in velocity, not speed. The magnitude doesn’t have to change in order for there to be an acceleration.
without steering input, your definition of acceleration would be correct, i.e. the acceleration vector will be in the same dimension as your direction of travel.
Even if speed remains constant, a change of direction is a change in the vector, which may be n-dimensional.
By virtue of your acknowledgement that there is a change of direction, you are also acknowledging that the body was acted upon by a force, since by newton’s law, everything should remain constant otherwise.
Changing heading means you introduce/ add a lateral vector into your original heading. If speed remains the same, the velocity in your original heading is actually reduced, even if your speed remains constant.
The change of direction is introduced by the interaction of the tyres and the road. Now that the tires have turned, a lateral force is introduced due to them no longer turning along the axis of minimum rolling resistance. The car responds by following the path of least resistance, which should follow the incidence direction of the tyres. Believe it or not, due to energy loss at the tyres your car will actually slow down during the turn without throttle input.
According to my buddy Newton, force experiences is equal to mass times acceleration
The mass you pretty much know is the mass of the car. The lateral force/ acceleration wouldn’t have happened without the steering.
The image says physicists, so yes, this isn’t as boring as it sounds, but it is an interesting thought experiment. Thanks for playing!
Lemme break it down for ya: