How can we derive the distance formula using velocity and acceleration?

In summary, The distance formula, S=vt+1/2at^2, can be derived from the velocity and acceleration formulas. It is also the solution to the differential equation where c is a constant. A graphical method can also be used to understand the formula by drawing a velocity-time graph. The area under the graph represents the displacement given by the formula.
  • #1
david12
5
0

Homework Statement



I try to drive distance formula which is S=vt+1/2at^2.



I use velocity and acceleration formula to drive the distance formula but i couldn't get the distance formula.is there anyone know how to drive S=vt+1/2at^2. and how that came from in the first place .

thank you.
 
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  • #2
Its the solution to the differential equation:

[tex]\frac{d^2s}{dt^2} = C [/tex]

where c is a constant.
 
  • #3
A more graphical method involves drawing a velocity-time graph of an object under constant acceleration from velocity u to v. It should look like a trapezium whose parallel sides are parallel to the velocity axis. The area of the parallelogram gives you the displacement, and that is given by the formula.
 

1. How do you prove or drive a scientific theory?

To prove or drive a scientific theory, a scientist must conduct experiments and collect data to support their hypothesis. This data should be analyzed and compared to previous findings to determine if the theory is valid. Additionally, the theory should be able to make accurate predictions and withstand further testing.

2. What is the difference between proof and evidence in science?

In science, proof refers to the ability to demonstrate that a theory is true beyond a reasonable doubt. This is usually achieved through rigorous testing and replication of results. Evidence, on the other hand, refers to the data that supports a hypothesis or theory. Evidence may be used to support a theory, but it is not considered proof until it has been thoroughly tested and validated.

3. How important is reproducibility in scientific proof?

Reproducibility is a crucial aspect of scientific proof. It refers to the ability of other scientists to replicate the same results and conclusions from an experiment. If a theory or hypothesis cannot be reproduced by other scientists, it is not considered a valid proof. Reproducibility ensures that scientific findings are reliable and not just a result of chance or error.

4. Can a theory ever be considered "proven" in science?

In science, a theory can never be considered 100% proven. This is because new evidence and advancements in technology may lead to a better understanding of a particular phenomenon, which can then lead to revisions or modifications of existing theories. However, a theory can be highly supported by evidence and withstand thorough testing, making it widely accepted by the scientific community.

5. How do scientists determine the validity of a proof?

Scientists determine the validity of a proof by subjecting it to peer review and further testing. Peer review involves having other experts in the field critically evaluate the research and findings to identify any flaws or biases. The proof should also be able to withstand rigorous testing and produce consistent results. Additionally, external factors and alternative explanations should be considered before accepting a proof as valid.

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