Graphs of a vs. t, v vs. t, and d vs. t ?

  • Thread starter IamHenry
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In summary, the graphs of a vs. t, v vs. t, and d vs. t are all related through basic equations and relationships between the variables. By studying the given graph of a vs. t and using the relationships between acceleration, velocity, and displacement, one can estimate the graphs of v vs. t and d vs. t by finding the area under the curve. It is important to note that the slope and position of the curves are determined by the values of acceleration, velocity, and displacement.
  • #1
IamHenry
Graphs of a vs. t, v vs. t, and d vs. t ?

Plese help !

I am given a graph of a vs. t
How do i use it to determine the other graphs:
v vs. t
d vs. t
 
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  • #2
You haven't supplied enough information. What are the relationships between the variables defined by the letters a,t,v,d?
 
  • #3
If you have the equations, just plug in a few points and go.

If you have one equation, you integrate to get the others... but like mathman said, you haven't given us enough information.
 
  • #4
i am not given any equations
i am only given the graph of a vs. t
btw
a=acceleration
t=time
v=velocity
d=displacement
please help
thx
 
  • #5
You need to use the basic relationships between the quanities.

a= dv/dt => The acceleration determines the slope of the velocity graph. So a constant acceleration line means an increasing velocity, Acceleration = 0 means a constant velocity. You must study the graphs you are given and piece together the various graphs.

Remember that v = dx/dt so you can do the same thing with the velocity line to create a displacement graph.

With that said this is off to homework.
 
  • #6
v = [inte] a dt

d = [inte] d dt
 
  • #7
If it's not a very screwed up graph you can write the equations just by looking at it.
 
  • #9
Probably what you want for this is the fact that the integral is the area under the curve.

Given a graph for a(t), estimate the area under the curve from 0 to t for a number of different values of t. That will give the graph for v(t). It is probably enough to remember things like: if the graph of a(t) is above a=0, then v(t) is increasing, if below, then v(t) is decreasing. if the graph of a(t) is horizontal, then v(t) increases (or decreases) linearly with slope given by the a value.

Once you have a rough graph for v(t), x(t) is the area under that curve. Repeat the process to get a graph of x(t).
 

1. What is the purpose of plotting graphs of a vs. t, v vs. t, and d vs. t?

The purpose of plotting these graphs is to visually represent the relationship between acceleration (a), velocity (v), and displacement (d) over time (t) for a given object or system. This allows for easier analysis and understanding of the motion or changes in motion over time.

2. How is time typically represented on these graphs?

Time is typically represented on the horizontal (x) axis of the graph, with each point or tick mark representing a specific increment of time, such as seconds, minutes, or hours.

3. What does the slope of a v vs. t graph represent?

The slope of a v vs. t graph represents the object's acceleration, as it is the change in velocity (v) over time (t). The steeper the slope, the greater the acceleration.

4. How can you determine an object's displacement from a d vs. t graph?

The displacement of an object can be determined by finding the area under the curve on a d vs. t graph. This can be done by dividing the graph into smaller shapes, such as rectangles or triangles, and calculating their individual areas. The sum of these areas will give the overall displacement.

5. What does a curve on a a vs. t graph indicate?

A curve on an a vs. t graph indicates that the acceleration of the object is changing over time. This could be due to various factors, such as a change in force or a non-uniform motion.

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