How do I derive the formula for free fall displacement?

In summary, the conversation discusses how to obtain the formula for free fall displacement, which is D = 1/2 g t^2. It is derived from the formula for uniformly accelerated motion by setting the initial velocity to zero and the acceleration to g. The importance of choosing the correct coordinate axis and understanding basic kinematic equations is also mentioned. The conversation concludes with the suggestion of drawing a velocity-time graph to find the displacement.
  • #1
Omar.Castillo
11
0
Hey could anyone help me out there to know how you get to the formula of free fall displacement. D= 1/2 x g x t^2? I really have no clue of how to get it using other formulas. I started using the D=Vi x T + 1/2 x A x T^2 but then I got stuck I didnt know which other formula to bring into cancel the variables I NEED HELP PLEASE :D
 
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  • #2
If you know the formula for uniformly accelerated motion ([itex]D = v_i t + 1/2 a t^2[/itex]), then you can get the formula you need by setting the initial speed to zero and the acceleration to g. That gives you [itex]D = 1/2 g t^2[/itex].
 
  • #3
It's also important to make the wise choice of the sense of the coordinate axis along the displacement. That is, assuming the [itex] \vec{g} [/itex] field is pointing downwards, choose the vertical axis with the same sense.

Daniel.
 
  • #4
There is no formula here . As Doc Al put it, the initial velocity has to be set to zero for the formula to be applicable , so the formula seems to be forced.It is better to get hold of the three basic kinematic equations rather than learning formulae for each and every situation.

BJ
 
  • #5
Try to draw the velocity-time graph. The area under the curve will give you the displacement.
 
  • #6
Thanks

Hey thanks to all you guys

I never did know you could set the initial velocity to zero! that solved the entire problem thank you. Now I am wondering why I never thought of that well anyways thanks guys
 
  • #7
yes initial velocity can be set to zero if the object stops of an instant, or if it starts from rest.
 

1. What is the process for deriving a formula?

The process for deriving a formula involves identifying the variables and their relationships, using mathematical concepts and equations to manipulate the variables, and checking the resulting formula for accuracy and validity.

2. What are the common steps in deriving a formula?

The common steps in deriving a formula include gathering data and information, analyzing the problem or situation, identifying relevant variables, creating a model or representation of the problem, manipulating the variables using mathematical operations, and testing the resulting formula.

3. How do I know if my derived formula is correct?

To ensure the accuracy of a derived formula, it is important to double-check the steps and calculations used to derive it. Additionally, the formula should be tested with a range of values for the variables to ensure it produces expected results.

4. What are some helpful tips for deriving a formula?

Some helpful tips for deriving a formula include clearly defining the problem and its goals, using appropriate mathematical concepts and equations, breaking down complex problems into smaller, more manageable parts, and seeking feedback and assistance from colleagues or experts.

5. Can a derived formula be used in other situations or fields?

In many cases, a derived formula can be applied to similar problems or situations in other fields. However, it is important to consider the specific variables and assumptions used in the derivation and determine if they are applicable to the new situation. Modifications may need to be made to the formula in order for it to be accurate and useful in a different context.

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