Integrating V = V(initial) + at

[Alem2000]

sorry i didnt use latex..I tried...its annoying


V=V(initial) + at...when you integrate both sides you get x=x(initial) + ..?
I had a little trouble trying to integrate the (at) do you use the uv-integral(v DV) theorem...well i used that and it and it didnt give me the second equation for constant a...near to it but off by two terms. Would anyone be kind enough to show me?

 

[Doc Al]

Somethings messed up with your formatting. Is your question how to get from this:
$$v = v_0 + at$$
to this:
$$x = x_0 + v_0 t + 1/2 a t^2$$
If so, it's straightforward integration, since v = dx/dt.

 

[Alem2000]

I understand the first two terms must give you x and x initial. But I can't seem to grasp where the rest..are you integrating from time initial to time t?

 

[Doc Al]

Yes, you are integrating both terms, $v_0$ and $a t$, from the initial time (t = 0) to t. $x_0$ is just the integration constant = initial position.