Vertical space and left alignment in Latex

[PainterGuy]

Hi,

How do I left align the text below? Also, how do I create vertical spaces above and below the line stating "Subbing the following expressions..."? Could you please help me with it?


To derive 14(ii) $m_{0} \gamma^{2} \frac{d^{2} y}{d t^{2}}=e E_{y}^{\prime}$ from 13(ii) $m_{0} \frac{d^{2} y^{\prime}}{d t^{\prime 2}}=e E_{y}^{\prime}$, should I proceed as follows.

$$\begin{aligned} &\frac{d^{2} y^{\prime}}{d\left(t^{\prime}\right)^{2}}=\frac{d t}{d t^{\prime}} \frac{d}{d t}\left[\frac{d t}{d t^{\prime}} \frac{d y^{\prime}}{d t}\right]\\ &\text { Subbing the following expressions in the expression above. }\\ &y^{\prime}=y \text { and } \frac{d t}{d t^{\prime}}=\frac{1}{\gamma\left(1-\frac{v}{c^{2}} \frac{d y}{d t}\right)} \end{aligned}$$

 

[S.G. Janssens]

It is not fully clear to me what you want. I would probably use two displayed equations, with the "Subbing..." line in between, like so:
---
$$
\frac{d^{2} y^{\prime}}{d\left(t^{\prime}\right)^{2}}=\frac{d t}{d t^{\prime}} \frac{d}{d t}\left[\frac{d t}{d t^{\prime}} \frac{d y^{\prime}}{d t}\right]
$$
Substituting the following expressions
$$
y^{\prime}=y \quad \text{and} \quad \frac{d t}{d t^{\prime}}=\frac{1}{\gamma\left(1-\frac{v}{c^{2}} \frac{d y}{d t}\right)}
$$
in the expression above...
---
I think this is the more standard way to format it. Incidentally, if you want to use sub-numbered equations (e.g. 1a, 1b, etc.) with text in between, look at the "subequations" environment of the ams-math package.