One way I’ve gotten some decent leverage in getting students to really initiate with goal-less problems in early kinematics problems is to ask, “If you had taken this trip with a GPS device, what summary trip information could it give you?”
As a class we generate a list of things the GPS device would or should be able to calculate like:
Time of Arrival
Duration of Trip
Total Distance Traveled
Average speed (while moving)
Average speed (during entire trip)
I usually tack on a few things, like it could tell us how far we are from where we started (and in what direction). I also say that a good one should also be able to make a graph. I may or may not introduce average velocity.
My job at some point is to connect each of these to formal language and algebraic symbols used in our text. Unfortunately, our text is sloppy with clock readings vs. time intervals. It’s also sloppy with displacement and position. So it’s a little difficult.
I also think it’s cool to have “average speed while moving” be something that the physics text book doesn’t have, and that we’ll have to completely invent our own way of calculating it.