For thinking Deleuze’s concepts of movement-image and time-image, consider the questions:
Can time exist apart from movement? Might time live some kind of life apart from movement? Or is time merely the measure of movement? If time might have a life other than being the measure of movement, can you describe how?
Consider the following as a start:
In one sense time seems to be nothing but a measure of movement. For instance, if you move your hand from resting on the table (point A) to resting on your thigh (point B) and you count two seconds during the movement, then it would seem time is nothing but the abstract division of movement into a series of uniform units (two in this case). You could say this way of thinking makes time the being-measured of movement, makes time subordinate to movement.
However, is there another way of thinking about time? Is there another mode of being where time becomes something that actually exists for itself (not as a mere abstraction subordinated to movement)? For instance, you have an hour to wait for the arrival by train of a loved one you haven’t seen in years. In this situation the very sense of time itself would seem to take on a character which cannot be subordinated to movement as in the above example. While waiting, diverse stretches of historical images reflect on and color each other in the form of a variety of memories, while one anticipates a new image of this person which will affect the meaning or trajectory of the past images, etc. All the while the movements of bodies around oneself are now clearly subordinated to time as a way being-historical in and for itself.
Deleuze’s philosophy of cinema is about exploring these two modes of cinematic or narrative construction: (1) movement-images (where time is subordinated to movement) and (2) time-images (where movement is subordinated to time).