Determining the value of a constant

In summary, the conversation discusses the derivation of a kinematics equation and how to determine the constant term in the equation. It is suggested to use the physical description of the situation and check for consistency in units. It is also mentioned that in the given example, the time derivative of displacement is velocity, which can help determine the constant term by setting time to 0.
  • #1
Calpalned
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Example 3 shows the derivation of one of the kinematics equations. I am quite familiar with it. At the part where it says dx/dt = gt + constant, how does one determine if constant = x_0 or v_0? Thank you.
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  • #2
You use the physical description of the situation ... in this case, just checking the units are consistent should work.
 
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  • #3
Simon Bridge said:
You use the physical description of the situation ... in this case, just checking the units are consistent should work.
That makes sense. Thanks!
 
  • #4
Since the constant term does not depend on time - you can always find the expression for it by putting ##t=0## into the equation.
In your example ##v=gt+c## you get ##v(0)=c## ... because you understand from the physics, that the time derivative of displacement is velocity.
 

1. What is a constant?

A constant is a fixed value that does not change during a particular process or experiment.

2. Why is it important to determine the value of a constant?

Determining the value of a constant is important because it allows for accurate and consistent results in scientific experiments. It also helps to establish a baseline for comparison in future experiments.

3. How do scientists determine the value of a constant?

Scientists determine the value of a constant through careful measurement and observation. They may also use mathematical equations and data analysis techniques.

4. Can the value of a constant change?

No, the value of a constant is fixed and does not change during a particular process or experiment. However, it may change in different contexts or experiments.

5. Are there different types of constants?

Yes, there are different types of constants in science, such as physical constants (e.g. speed of light), mathematical constants (e.g. pi), and experimental constants (e.g. gravitational constant).

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