Conceptual Area Under Velocity-Time graph confusion

In summary, The area under a velocity-time graph can be treated as negative when it is below the x-axis, as the velocity in this region is also negative. This means that the displacement is calculated by subtracting the negative area from the positive area above the x-axis. However, some may prefer to simply subtract the areas regardless of the sign of the velocity, resulting in the same answer. This concept can also be compared to acceleration and deceleration, where negative acceleration is considered deceleration.
  • #1
zabachi
33
0
Hi all I have a confusion regarding a physics concept. When you consider area under graph (velocity time graph), if the area is below x axis, is the area considered to be negative?
For example, look at the attachment. There are 2 shaded areas. Let the area above x-axis be A and area below x-axis be B and ignore all the numerical values on the graph. Is the displacement A+B or A-B? I am very confused.
 
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  • #2
I can't see your attachment but I can say that you can treat areas under the x-axis as negative (after all, the velocity IS negative, isn't it? - so a positive time times a negative velocity gives you a negative answer.). So A+(a negative)B is the total area.
Alternatively, and less strictly mathematically, you can just subtract the areas underneath from the areas on top. Same answer, of course.
 
  • #3
The displacement is A-B, the distance is A+B.
 
  • #4
MikeyW said:
The displacement is A-B, the distance is A+B.

Only if you neglect that areas below the x-axis are negative.
 
  • #5
I don't agree, areas are always positive or zero.
 
  • #6
MikeyW said:
I don't agree, areas are always positive or zero.

I guess it's only a matter of taste but x times y will be negative if y is negative, surely?

If you were using a computer to calculate displacement from a set of v,t coordinates, would you have a special routine to spot negative velocity sections and then 'subtract' them? I think you would, more likely, just add em all up with regard to the sign of the v.

Would you also think of having 'acceleration' and 'deceleration', rather than positive and negative acceleration? There is a direct parallel there.
 

1. What is the conceptual area under a velocity-time graph?

The conceptual area under a velocity-time graph represents the displacement of an object over a certain amount of time. It is the total distance traveled by the object during that time period.

2. How is the area under the velocity-time graph related to the object's velocity?

The area under the velocity-time graph is directly proportional to the object's average velocity during the time period. A larger area indicates a greater average velocity, while a smaller area indicates a lower average velocity.

3. Can the area under a velocity-time graph be negative?

Yes, the area under a velocity-time graph can be negative. This occurs when the object is moving in the opposite direction, or when it changes direction during the time period.

4. How can I calculate the area under a velocity-time graph?

The area under a velocity-time graph can be calculated by dividing the graph into smaller shapes, such as rectangles or triangles, and then finding the area of each shape using basic geometry formulas. The sum of these areas will give the total area under the graph.

5. What are some real-life applications of understanding the area under a velocity-time graph?

Understanding the area under a velocity-time graph is important in various fields such as physics, engineering, and transportation. For example, it can be used to calculate the distance traveled by a car during a certain time period, or to determine the average speed of a rollercoaster during a ride.

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