The discussion revolves around understanding the relationship between area under a velocity-time graph and its implications for displacement and distance. Participants explore the definitions and interpretations of these concepts in the context of physics and mathematics.
The conversation includes various perspectives on the interpretation of negative areas in relation to velocity and displacement. Some participants suggest that familiarity with integration is not essential for understanding the concepts, while others argue that it is crucial for addressing the nuances of the question.
There appears to be a division in understanding among participants regarding the implications of negative areas on a velocity-time graph, particularly for those unfamiliar with integration. This highlights the varying levels of background knowledge in the discussion.
The area under a curve is always, by definition, a positive number. If a curve crosses the ##x## axis, then the total area between the curve and ##x## axis is the sum of all the separate areas.grzz said:Homework Statement:: Is area under a velocity-time graph a distance or displacement?
Relevant Equations:: Velocity = rate of change of displacement with time.
I think the area required is a displacement.
Not necessarily. You can take an area below the ##x## axis to be negative, without relying on integration.grzz said:Hence such a question makes sense only to students who are familiar with integration. Am I correct to say this?
If we are talking about a velocity-time graph, then velocity is negative below the time axis. And displacement is negative. That is nothing to do with integration.grzz said:A student who knows about integration will not ask why the area can be negative while one who does not know about integration will ask why the area below the x axis is negative. What answer can I give him then?