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)

Verified step by step guidance

1. Start with the given formula: \( s = \frac{1}{2}gt^2 \).
2. To solve for \( g \), first isolate \( g \) by multiplying both sides of the equation by 2 to eliminate the fraction: \( 2s = gt^2 \).
3. Next, divide both sides by \( t^2 \) to solve for \( g \): \( g = \frac{2s}{t^2} \).
4. Ensure that \( t \neq 0 \) to avoid division by zero, as specified in the problem.
5. The formula \( g = \frac{2s}{t^2} \) now expresses \( g \) in terms of \( s \) and \( t \).

Key Concepts

Algebraic Manipulation

Algebraic manipulation involves rearranging equations to isolate a specific variable. This process includes operations such as addition, subtraction, multiplication, and division applied to both sides of the equation. Understanding how to manipulate equations is essential for solving for variables in formulas.

Quadratic Relationships

The formula s = 1/2gt² represents a quadratic relationship between distance (s) and time (t) when an object is in free fall. In this context, g is the acceleration due to gravity. Recognizing the nature of quadratic equations helps in understanding how variables interact and how to isolate them effectively.

Assumptions in Equations

When solving equations, it is crucial to consider any assumptions, such as the condition that the denominator is not zero. This ensures that the solutions are valid within the context of the problem. Acknowledging these assumptions helps prevent mathematical errors and ensures the integrity of the solution.