Question

Solve the formula h = 54t + 1/2 * a * t ^ 2 for a.

Answer 1

The initial equation is:

$h=54t+\frac{1}{2}at^2$

First, we subtract 54t on both sides as:

$\begin{gathered} h-54t=54t+\frac{1}{2}at^2-54t \\ h-54t=\frac{1}{2}at^2 \end{gathered}$

Multiplying by 2, on both sides:

$\begin{gathered} 2\cdot(h-54t)=2\cdot\frac{1}{2}at^2 \\ 2h-108t=at^2 \end{gathered}$

Dividing by t^2, we get:

$\begin{gathered} \frac{2h-108t}{t^2}=\frac{at^2}{t^2} \\ \frac{2h}{t^2}-\frac{108}{t}=a \end{gathered}$

Answer:

$a=\frac{2h}{t^2}-\frac{108}{t}$