Pattar, Curve acceleration

Is it true or does the swing follow the same science, that a car going into a turn decelerates and it takes more energy/force to maintain speed? Does the curve/turn decelerate the car? And if so does the early arc/curve in the swing require more force to accelerate the bat? Is that the reason for early batspeed needed in the swing?

Not sure what you are referring to when you say a car decelerates when going into a turn. To maintain the speed of a car, around a curve or not, the force from the engine needs to balance the opposing force which is the drag. The drag is approximately proportional to the velocity of the car squared and has nothing to do with whether the car is in a turn or not. What does happen when you go around a curve is that their is an acceleration component, perpendicular to the motion, which comes from the change of direction of the car. The force from this acceleration is equal to the friction force on the surface if the car doesn't slip. Same idea with a swing. You apply a force at the hand initially to accelerate the bat and to maintain a constant velocity the gravitational force and force applied by the hitter on the handle needs to balance the drag force. There is also an acceleration perpendicular to the motion of the bat except in this case that there is no friction force and instead a tension in the bat is induced which really doesn't effect anything since the bat is fairly rigid (e.g.. the hitter would not notice a pull on his hands from this).

With regards to early bat speed, I just think that the position a hitter is in which generates early bat speed is optimal in terms of both the force the hitter is able to apply to the handle initially and the bat path which is
generated from this position. Also the time it takes from swing launch to contact is proportional to the integral around the bat path of the inverse of the velocity at each point on this path so early bat speed (e.g. high velocity a points
close to the beginning of the bat path) along with a bat path made possible by a position at launch which generates early bat speed, may be close to optimal in terms of time to contact.