I have read at many places that you should rapidly prototype to know feasibility of idea. What is an acceptable time taken for creating a prototype? Is a prototype different from a web application launching in private beta?
I don't think there's any such thing as an acceptable amount of time to create a prototype. The amount of passion you have for the idea and the other parts of your life that take your time will feed into how long it will take to create a prototype.<p>I would say a prototype and a private beta can be synonymous but it is more likely that a prototype would develop into something more substantial which you would then look to publicise and get more feedback from with a private beta.<p>A prototype is more likely to be along the lines of something you would show to relevant folk on a narrower basis than a private beta, to gauge whether they would be interested in the product.
You should have a broken, buggy POC in 2-5 days, something that you can actually log into in 2-6 weeks, and something someone would actually pay for in 4-6 months.