Difference between position time, velocity time and acceleration time graph

In summary, the difference between a position time graph, velocity time graph, and acceleration time graph lies in the relationship between the plotted variables. The position time graph shows the change in position over time, while the velocity time graph represents the change in velocity over time, and the acceleration time graph displays the change in acceleration over time. Each graph has a unique shape, with the position time graph being exponential, the velocity time graph being a ramp, and the acceleration time graph being a horizontal straight line. These relationships can also be seen when integrating and differentiating the graphs.
  • #1
h2chawwaa
1
0
What is the difference between position time graph, velocity time graph and acceleration time graph and how would each of them look like when drawn?
 
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  • #2
h2chawwaa said:
What is the difference between position time graph, velocity time graph and acceleration time graph and how would each of them look like when drawn?

exponential, ramp,straight line parallel to time axis
 
  • #3
Change of position per unit time is motion and hence, there is velocity there...for as long as velocity is the rate of change of position vs time, we can say that velocity is the derivative of position vs time curve.

Acceleration is the rate of change of velocity per unit time...and so, acceleration is the derivative of the velocity vs time curve.

So, if something is not moving, and it has the same position at all times (horizontal line in y vs t plot), vel=0, acc=0

If something is moving at a constant rate, the plot is an inclined line..its derivative is a constant (slope) which is the speed. The derivative of a constant (speed) is zero (acc=0).

If something is moving at various speeds/acceleration, the position plot will be all over the place, the velocity will be the derivative of such curve, and acceleration that derivative of the speed curve.
 
  • #4
There are also relationships when integrating velocity as a function of time and acceleration as a function of time.
 
  • #5
easwaran.sr said:
exponential, ramp,straight line parallel to time axis

If the object is moving at constant acceleration then the plot of position versus time is exponential, a plot of velocity vs time is a ramp ( ie sloped ), and the plot of acceleration vs time is a horizontal straight line.

If the object is moving at a constant velocity then the plots become a ramp, a horizontal line, and a horizontal line with acceleration = 0.

If the object has no velocity nor acceleration then the plot of position is a horizontal staright line and the plots of both velocity and acceleration are horizontal straight lines with velocity=0 and acceleration=0.
 
  • #6
256bits said:
If the object is moving at constant acceleration then the plot of position versus time is exponential ...
It would be quadratic, x(t) = x0 + v0 t + 1/2 a t2.
 
  • #7
256bits said:
If the object is moving at constant acceleration then the plot of position versus time is exponential, a plot of velocity vs time is a ramp ( ie sloped ), and the plot of acceleration vs time is a horizontal straight line.

If the object is moving at a constant velocity then the plots become a ramp, a horizontal line, and a horizontal line with acceleration = 0.

If the object has no velocity nor acceleration then the plot of position is a horizontal staright line and the plots of both velocity and acceleration are horizontal straight lines with velocity=0 and acceleration=0.

the derivative of an exponential is another expenetial which is clearly not what happens when you differentiate the d-t graph of a uniformally accelerated object, it has to be quadratic, which leads to a linear v-t graph when differentiated and then when differentiated the second time to a horrizontal line
 

1. What is the difference between a position-time graph and a velocity-time graph?

A position-time graph shows the change in an object's position over time, while a velocity-time graph shows the change in an object's velocity over time. In other words, a position-time graph shows the distance an object has traveled, while a velocity-time graph shows the speed at which the object is traveling.

2. How can you determine an object's acceleration from a velocity-time graph?

The slope of a velocity-time graph represents an object's acceleration. A steeper slope indicates a greater acceleration, while a flatter slope indicates a smaller acceleration. The units for acceleration on a velocity-time graph are meters per second squared (m/s^2).

3. How do you find an object's displacement from a position-time graph?

The displacement of an object can be found by calculating the area under the curve of a position-time graph. This can be done by dividing the graph into smaller shapes (such as rectangles or triangles) and adding up their individual areas. The resulting value is the object's displacement.

4. How is the motion of an object represented on an acceleration-time graph?

An acceleration-time graph shows the change in an object's acceleration over time. The slope of the graph represents the rate of change in acceleration, and the area under the curve represents the change in velocity. A flat line on an acceleration-time graph indicates a constant acceleration, while a curved line indicates a changing acceleration.

5. What can you determine about an object's motion from a position-time, velocity-time, and acceleration-time graph?

From a position-time graph, you can determine an object's distance traveled and its direction of motion. From a velocity-time graph, you can determine an object's speed and acceleration. From an acceleration-time graph, you can determine how an object's acceleration changes over time. All three graphs together provide a comprehensive understanding of an object's motion.

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