My ds is just 20 months old and and is starting to get quite physical - mostly with his big sister, but recently he's started pushing other children at the park if they are in his way. It's a shock as dd didn't go through this stage. She was a gentle little thing and was more likely to be the victim of other toddlers' aggression. I haven't parented them any differently, so I can only assume this is due to a difference in temperament.
I am dealing with it with a firm 'no' and swiftly removing him from the situation. I don't think he has enough understanding to grasp any more long-term consequences. I tell him 'no hitting, it hurts', which I think he understands, and he knows that I am unhappy with his behaviour. I'm not sure what else can be done. Hopefully this is a phase which will pass soon!