I need some help here - I don't get what's going on
What's happening between the two steps? It would be nice with an extra step or two, as this is very hard for me..
On the right hand side, the integration is simple, with A being the constant of integration, so I imagine you're asking about what they did on the left hand side.
First, they used the fact that to get
Next, you use the method of partial fractions:
for some A, B.
To find A and B, we multiply this by to get:
Equating the coefficients of powers of v, we get and
This gives and . Thus:
Now, note that , so ,
Then you use the fact that to get
which is the left hand side of their result.
Now, as to your question:
If we have an expression, say
that is supposed to be true for all values of v, then we can say that A = 0 and B = 1. This is the only possible solution for A and B.
This technique generalizes. Suppose instead we have something like
that is true for all v. (Notice that this condition is critical!) Then we may say that
C=0,0067 and g = 9,82, and I guess A=0 (or what???)
What is wrong? This function is decreasing, but it's a velocity-function, it should be increasing!!
Help, it's for thursday and a big subject!!
I made a slight error in integrating this. It should be a Riemann integral with the intial condition v(0) = 0:
In other words, the A vanishes.
Now, the problem I am having is that v is not defined at t = 0! But v(0) = 0 has already been applied to the Riemann integral. I have no explanation of why this is happening.