Hi, I will try and help you with this ....
Thank you so much
When we look at different parenting styles coping skills will differ. If a child was allowed to explore, with limits their environment they will as adults be the best adjusted (authoritative). They are the most well adjusted adults. Permissive parenting leaves the child to figure out their own environment, they as adults may cope by doing what they wish, no one ever taught them it's okay or not okay to do something, no boundaries, no rules and they may interpret as no one caring.
authoritarian parenting makes nervous adults (short answer). Compliant as children they mature with doubt, they have never been able to test the waters (so to speak), they were told what to do, how to do it and when to do it. They had no voice in decisions, no democratic interaction.
I am not sure what effect they would have on physical development, need to think about that.
What you need to do to write this up is to look at the definitions of each style, take one specific hypothetical situation and compare the behavior of the three. It could be a social situation (probably easiest) and then talk about personality differences due to parenting styles. You can also look at developmental stages and talk about how each style affects social/personality issues. For example, during the teen years each one of these styles will affect the teen differently. The permissive style will be the teen who can stay out without any rules, the authoritative will negotiate what is best for the teen (home at ??) while the authoritarian style will tell the teen what to do and when to come home, no negotiations. Then describe how you think that affects them as adults....who will be okay, who will not be able to make a decision easily and so on.
As for physical development, one of the areas that may be affected is eating. If a child is allowed to eat whatever they want, they may not be eating what is needed for optimal growth and development (permissive). Authoritatian parents may insist on the child eating whatever is put in front of them and this control may be met with resistance which in turn may result in eating disorder. Authoritative style allows the child to have a say in what they eat, and is allowed to have choices, but parents make sure the diet meets nutritional needs. As adults these early experiences can have a large impact on how they view food (which is only one physical aspect but the best and simplest example).
hope this helps get you started and gives you more understanding.