The initial equation is:
[tex]h=54t+\frac{1}{2}at^2[/tex]First, we subtract 54t on both sides as:
[tex]\begin{gathered} h-54t=54t+\frac{1}{2}at^2-54t \\ h-54t=\frac{1}{2}at^2 \end{gathered}[/tex]Multiplying by 2, on both sides:
[tex]\begin{gathered} 2\cdot(h-54t)=2\cdot\frac{1}{2}at^2 \\ 2h-108t=at^2 \end{gathered}[/tex]Dividing by t^2, we get:
[tex]\begin{gathered} \frac{2h-108t}{t^2}=\frac{at^2}{t^2} \\ \frac{2h}{t^2}-\frac{108}{t}=a \end{gathered}[/tex]Answer:
[tex]a=\frac{2h}{t^2}-\frac{108}{t}[/tex]