Solve each formula for the specified variable. Assume that the denominator is not 0 if variables appear in the denominator. s = 1/2gt², for g (distance traveled by a falling object)

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Start with the given formula: \(s = \frac{1}{2} g t^{2}\).

To isolate \(g\), first eliminate the fraction by multiplying both sides of the equation by 2: \(2s = g t^{2}\).

Next, to solve for \(g\), divide both sides of the equation by \(t^{2}\) (assuming \(t \neq 0\)): \(\frac{2s}{t^{2}} = g\).

Rewrite the equation to clearly express \(g\) as the subject: \(g = \frac{2s}{t^{2}}\).

This is the formula for \(g\) in terms of \(s\) and \(t\).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Solving Formulas for a Specific Variable

This involves rearranging an equation to isolate the desired variable on one side. It requires using inverse operations such as multiplication, division, addition, subtraction, and taking roots to rewrite the formula in terms of the specified variable.

Understanding Variables and Constants in Physics Formulas

In the formula s = 1/2gt², s represents distance, g is acceleration due to gravity, and t is time. Recognizing which variables are constants or given values helps in correctly manipulating the formula and interpreting the physical meaning.

Handling Exponents and Square Roots

Since t is squared in the formula, solving for g requires understanding how to deal with exponents. This often involves isolating the squared term and then applying square roots or squaring both sides to simplify the equation.

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