Question (1 Viewer)

[azureus88]

[maths]x=\int_{0}^{t}vdt[/maths]

Does this apply for any function v? Also, what is the proof/explanation to this?

Thanks

 

[jet]

Well, start with the definition that:

where x is displacement and v is velocity, both as functions of time. Now, I would be careful about how you have expressed the LHS above, as the object may not have started off at the origin, and so you cannot assume that fact. Working from the definition above,


Now, lets assume that the object begins at any displacement, call it
Then, when
So, at any time, the object could be at any displacement. So, these are the limits on our integral:


You can see that you have assumed .

Also, it is important to note that both v must be a function of t in that example, as we are integrating with respect to t.

 

[Affinity]

[maths]x=\int_{0}^{t}vdt[/maths]

Does this apply for any function v? Also, what is the proof/explanation to this?

Thanks

Fundamental theorem of calculus - Wikipedia, the free encyclopedia

It applies to any function you can think of.

 

[Kurwa]

its strictly with respect to t i.e time =]