Coefficients for the equation of the position vs time equation

In summary: Differentiate again and you getd²y/dt² = 0 which is the acceleration. In summary, the conversation discusses a physics lab on kinematics and finding the position, speed, and acceleration of a moving object. The equations used are for a position vs time graph and the question asks about the relation of the coefficient of the x^2 term to the graphs of speed vs time and acceleration vs time. The answer is that it is equivalent to 1/2 the slope of the speed vs time graph, which can be understood by differentiating the position equation. Similarly, the relation of the coefficient of the x-term to the graphs of speed vs time and acceleration vs time is that it is equivalent to the y-inter
  • #1
EDIT: I figured it out by looking at this link pages 65-66. Thanks for looking though! http://www.bfasta.net/assets/files/...46 Information/HSU/Chapter 4 Acceleration.pdf

Homework Statement


Recently I just did a physics lab for kinematics in which we found the position, speed, and acceleration as time passed of a moving object. I finished most of the lab questions, however am curious about 2 aspects of the equation.


Homework Equations



Position vs time graph equation: [tex]y = 0.5424x^2 + 0.2072x + 0.0149[/tex]

The Attempt at a Solution


One of the questions asks the relation of the coefficient of the x^2 term to the graph of the speed vs time and the graph of the acceleration vs time. I figured out that it's 1/2 the slope of the speed vs time/equivalent to the acceleration, so I finished the question. However, I have no clue why this is true (this isn't part of the lab question, I'm just curious).

Another question asks how the coefficient of the x-term relates to the graph of the speed vs time and acceleration vs time. I already figured out that it is equivalent to the y-intercept of the speed vs time graph, but am not sure if it relates to the acceleration vs time graph. The only relation I can see is that it is about 1/5 of the y-intercept of the acceleration equation. Is this correct? (And why, if it is).


EDIT: I figured it out by looking at this link pages 65-66. Thanks for looking though! http://www.bfasta.net/assets/files/...46 Information/HSU/Chapter 4 Acceleration.pdf
 
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  • #2
I assume "x" in that equation is "time"? In which case..

If that's the equation for position then differentiate it and you get the equation for the velocity. Differentiate it again and you get the equation for acceleration.

I suggest doing that and then plotting the graphs. The coefficients may make more sense.

For example consider the standard straight line equation

y=mt + c

m is the slope of the "curve". Differentiate wrt t and you get

dy/dt = m

but dy/dt is a velocity so the coefficient m is the velocity.
 
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1. What is a coefficient in the position vs time equation?

A coefficient is a numerical value that indicates the relationship between the position and time variables in an equation. It can be positive, negative, or zero. In the position vs time equation, the coefficient represents the rate of change of position over time, also known as velocity.

2. How is the coefficient calculated in the position vs time equation?

The coefficient in the position vs time equation is calculated by dividing the change in position by the change in time. This can also be thought of as the slope of the position vs time graph.

3. Can the coefficient in the position vs time equation be negative?

Yes, the coefficient in the position vs time equation can be negative. This indicates that the position is changing in a negative direction, or in other words, the object is moving in the opposite direction of the positive direction on the position axis.

4. What does a coefficient of zero mean in the position vs time equation?

A coefficient of zero in the position vs time equation means that there is no change in position over time, or the object is at rest. This can also be represented by a horizontal line on the position vs time graph.

5. How does the coefficient affect the position vs time graph?

The coefficient in the position vs time equation determines the slope of the position vs time graph. A larger coefficient indicates a steeper slope, meaning a greater rate of change in position over time. A smaller coefficient indicates a gentler slope, meaning a slower rate of change in position over time. A coefficient of zero results in a horizontal line on the position vs time graph, representing no change in position over time.

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