Interpreting Graphs: Position, Velocity & Acceleration

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In summary, position v. time graphs show displacement, acceleration v. time graphs show velocity, and velocity graphs or equations can determine relative position but not absolute position without additional information.
  • #1
azn4lyf89
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I can't post up the graph but I just need some help with general ideas. If I have a position v. time graph will the area under the curve be the acceleration? Also, in an acceleration v. time graph does the area under the curve represent anything? And if I have a velocity graph or velocity equation do I have enough information to determine a position at a given time without knowing any positions?
 
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  • #2
azn4lyf89 said:
I can't post up the graph but I just need some help with general ideas. If I have a position v. time graph will the area under the curve be the acceleration? Also, in an acceleration v. time graph does the area under the curve represent anything? And if I have a velocity graph or velocity equation do I have enough information to determine a position at a given time without knowing any positions?

In a position v time graph the area under the curve is displacement.
The tangent (or slope) at any point is the velocity (rate of displacement change).
The area under an acceleration v time graph will yield the velocity across the time interval.
Velocity is a rate of change of displacement. You can determine a relative position over a time interval, but not an absolute one without knowledge of some position.
 
  • #3


I can provide some insights and clarifications on interpreting graphs of position, velocity, and acceleration.

Firstly, in a position vs. time graph, the area under the curve does not represent acceleration. The slope of the curve at any given point represents the instantaneous velocity at that point. To calculate acceleration, we need to take the derivative of the velocity function, which is represented by the slope of the position vs. time curve.

In an acceleration vs. time graph, the area under the curve does represent something. It represents the change in velocity over a certain time interval. This is because acceleration is the rate of change of velocity over time. Therefore, the area under the curve can give us information about the change in velocity over a specific time period.

If you have a velocity graph or equation, you do not have enough information to determine position at a given time without knowing any positions. This is because velocity is the rate of change of position over time. Without any information about the initial position, we cannot accurately determine the position at a specific time.

I hope this helps clarify some of your questions about interpreting graphs of position, velocity, and acceleration. Remember, these graphs are tools that help us visualize and understand the relationships between these important quantities in physics.
 

What is the difference between position, velocity, and acceleration?

Position is the location of an object at a specific point in time. Velocity is the rate at which an object's position changes over time. Acceleration is the rate at which an object's velocity changes over time.

How are position, velocity, and acceleration related?

Position, velocity, and acceleration are all related through the equations of motion. Velocity is the derivative of position, and acceleration is the derivative of velocity.

How can I interpret a position-time graph?

A position-time graph shows the position of an object over time. The slope of the graph at any point represents the velocity of the object at that time. The area under the graph represents the displacement of the object.

How can I interpret a velocity-time graph?

A velocity-time graph shows the velocity of an object over time. The slope of the graph at any point represents the acceleration of the object at that time. The area under the graph represents the displacement of the object.

What can I learn from an acceleration-time graph?

An acceleration-time graph shows the acceleration of an object over time. The slope of the graph represents the rate at which the acceleration is changing. The area under the graph represents the change in velocity of the object.

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