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Yes, this would be a useful feature, in my opinion. Not a check-box as WORDS implies, but an invitation to state (in WORDS!) what steps have been taken to undertake the expected "prior research". Thus reminding the OP of his/her obligations.

I suggested the same feature myself a couple of months ago, but I cannot find where it was that I did so. Perhaps in a comment. (Yes, I know - "answering in comments"!)

Update in Response to Comments

Do you envision this applying only to prospective homework questions, or to all new users' first question? – Emilio Pisanty

I would expect the feature to apply to all questions, irrespective of rep or type of question. I see no justification for discriminating in either case. All users would benefit from the reminder. My understanding is that all questions should show some prior research effort, not only those which are "homework-like". Users who have made the effort will not mind stating what they've done; those who aren't willing to make any effort will hopefully go away!

I would suggest it apply to users with less than 100 rep, somewhere where the users are sort of established.– heather

I suggest that it should apply to all users, because
1. I have seen users with >1k rep post questions without making any internet search - perhaps high reps post so few questions that they need the reminder?;
2. it helps the OP try to resolve his/her own problem and narrow down the difficulty;
3. it lets potential answerers know what has already been tried, so that they do not waste effort doing the same;
4. discrimination should be avoided wherever possible.

Many already provide this information in the question, so it should be no additional burden to them.

What if the requirements decreased for higher rep users? – heather

I think the feature should operate uniformly, the same for everyone, unless there is a good reason to do otherwise. It could include check boxes for "searched this site for duplicates" and "searched the internet," to minimize typing. I think asking them to confirm they have "read help centre info" is too broad a request and too burdensome. The feature itself should remind the OP - as succinctly as possible - of the minimum requirements for "prior research/effort".

A typed description should be mandatory - but with a low minimum of perhaps only 30 characters. Requiring an essay will not be received well. The OP should decide how much is appropriate.

The purpose of the feature is (1) to remind the OP of his/her obligation to ensure the question is "on topic", and (2) to elicit useful information which will guide potential answerers.

Note: I have focussed on the "prior research effort" requirement, but the "appropriate subject" requirement ("asking about a specific concept of physics") should not be forgotten in the feature.