Question

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

Answer 1

The initial equation is:

`h=54t+(1)/(2)at^2`

First, we subtract 54t on both sides as:

`\begin{gathered} h-54t=54t+(1)/(2)at^2-54t \\ h-54t=(1)/(2)at^2 \end{gathered}`

Multiplying by 2, on both sides:

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

Dividing by t^2, we get:

`\begin{gathered} (2h-108t)/(t^2)=(at^2)/(t^2) \\ (2h)/(t^2)-(108)/(t)=a \end{gathered}`

Answer:

`a=(2h)/(t^2)-(108)/(t)`