Lets say we have a car, with power being given to maintain it at 100 km/h and about to negotiate a slight bend. As the car turns the corner, there is no change to the accelerator pedal, and no braking. All wheels maintain full traction. Let's assume it has completely stiff suspension (ie none) and the road is a perfectly flat surface.
Will this car slow down? If so, why? Racing cars still maintain a racing line (as straight as possible) through corners they can go flat out with full traction through, which is longer (but apparently faster) than if they hugged the inside corner. Why? What is the actual physical reason that causes cars to slow down in corners? Correct me if any of my assumptions are wrong.