Area under acceleration-time graph?

  • Thread starter tahayassen
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    Area Graph
In summary, the area under an acceleration-time graph gives the change in velocity between two points in time, with one point being the present time and the other being the initial time. This is also known as instantaneous velocity.
  • #1
tahayassen
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Homework Statement



What does the area under an acceleration-time graph give?

Homework Equations





The Attempt at a Solution



Instantaneous velocity.
 
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  • #2
hi tahayassen! :smile:
tahayassen said:
What does the area under an acceleration-time graph give?

Instantaneous velocity.

strictly, instantaneous velocity minus initial velocity :wink:
 
  • #3
tiny-tim said:
hi tahayassen! :smile:


strictly, instantaneous velocity minus initial velocity :wink:

Oh, because it gives you the change in velocity. Opps!
 
  • #4
Actually, which initial velocity are we talking about? The initial velocity of that instant?
 
  • #5
"the area under" must mean "between two values of t" …

one value is the present time, the other value is what we usually call the initial time :wink:
 

What is the definition of "area under acceleration-time graph?"

The area under an acceleration-time graph represents the change in velocity over a certain period of time. It is measured in units of meters per second squared (m/s^2).

How is the area under an acceleration-time graph calculated?

The area under an acceleration-time graph can be calculated by dividing the graph into smaller sections, calculating the area of each section, and then adding all of the areas together. Alternatively, it can be calculated using calculus by integrating the acceleration function over time.

What does the sign of the area under an acceleration-time graph indicate?

The sign of the area under an acceleration-time graph indicates the direction of the acceleration. A positive area indicates a positive acceleration (speeding up), while a negative area indicates a negative acceleration (slowing down).

How does the area under an acceleration-time graph relate to an object's displacement?

The area under an acceleration-time graph represents the change in velocity, and the displacement of an object is directly related to its velocity. Therefore, the area under an acceleration-time graph can be used to calculate an object's displacement over a certain period of time.

What are some real-life applications of understanding the area under an acceleration-time graph?

Understanding the area under an acceleration-time graph is important in various fields such as physics, engineering, and sports. It can be used to analyze the motion of objects, design efficient transportation systems, and improve athletic performance by studying acceleration and speed.

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