Deriving the Equation for Final Velocity Using Kinematic Equations

  • Thread starter zeion
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In summary, the process for deriving an equation involves using known principles and laws and manipulating them mathematically to arrive at the desired equation. The principles and laws used depend on the specific problem and a solid understanding of relevant concepts is important. Multiple methods can be used to derive the same equation. To check the validity of a derived equation, known values can be plugged in or it can be compared to existing equations or principles. It is generally recommended to show all the steps in deriving an equation for clarity and understanding.
  • #1
zeion
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Homework Statement



I wanted to know how this equation is derived. Thanks.

Homework Equations



[tex] {v_{f}}^2 = {v_{i}}^2 + 2a\Delta d [/tex]

The Attempt at a Solution



[tex] v_{f} - v_{i} = \frac {\Delta d a} {\Delta v} [/tex]
 
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  • #2
We have the two relations:
[tex]t=\frac{v-u}{t}[/tex]
[tex]s=\frac{1}{2}(u+v)t[/tex]

Substitute the first into the second and the deed is done.
 
  • #3
Start from:
1. v=vo+at
2. r=ro+vo*t+(at^2)/2
Find t from 1 and replace in 2, do all the algebra and you are done.
 

1. What is the process for deriving an equation?

The process for deriving an equation involves starting with a known set of principles or laws and using mathematical manipulation and reasoning to arrive at the desired equation.

2. How do I know which principles or laws to use when deriving an equation?

The principles and laws used in deriving an equation depend on the specific problem you are trying to solve. It is important to have a solid understanding of the relevant concepts and theories in order to choose the appropriate ones.

3. Can I use different methods to derive the same equation?

Yes, there are often multiple ways to derive the same equation. The method used may depend on personal preference or the specific problem at hand.

4. How can I check if my derived equation is correct?

One way to check the validity of a derived equation is to plug in known values and see if the resulting equation holds true. Another way is to compare it to existing equations or principles in the field.

5. Is it necessary to show all the steps in deriving an equation?

It is generally recommended to show all the steps in deriving an equation, as it helps to clearly explain the thought process and make it easier for others to understand and replicate the derivation.

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