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?
Negative velocity on a velocity-time graph indicates that the object is moving in the opposite direction to the positive reference direction. It does not mean the object is slowing down; rather, it is traveling in the reverse direction.
Displacement is determined by calculating the area under the velocity-time graph. If the velocity is negative, the area under the curve will be below the time axis, contributing a negative value to the total displacement. Sum both positive and negative areas to find the net displacement.
A negative slope on a velocity-time graph represents a negative acceleration, meaning the object is decelerating if moving in the positive direction or accelerating if moving in the negative direction.
Yes, an object can have a negative velocity and a positive displacement. This situation occurs when the object initially moves in the positive direction, accumulating positive displacement, and then reverses direction, moving with a negative velocity.
When the velocity crosses from positive to negative on a velocity-time graph, it indicates that the object has changed direction. The point where the velocity crosses the time axis (velocity equals zero) represents the moment when the object stops and reverses its direction of motion.