For such a short distance, A scooter or a pair of shoes is the answer. (I live about 2.5km from work as well, so I'm in the same boat)
I recommend a Honda Vision, or if you really have some hangup about scooters, a Honda e-storm. The scooter is a lot more practical though, plenty of storage space for your lunchbox.
I can fit 2 six-packs and a bottle of wine under my scooter seat, and a bag of wood under my legs. +- R50 of petrol every 2 weeks. That's my total commuting budget.