Chapter 1.4, Problem 34PPSE

Solution

To solve the equation $s=\frac{1}{2}g{t}^2$ for g .

  $g=\frac{2s}{t^2}$

Given:

The equation, $s=\frac{1}{2}g{t}^2$ .

Concept Used:

• The opposite operation of addition is subtraction and the opposite operation of subtraction is addition.
• The opposite operation of multiplication is division and the opposite operation of division is multiplication.
• Distributive property: $a\left(b+c\right)=a\cdot b+a\cdot c$

Calculation:

In order to solve the given equation $s=\frac{1}{2}g{t}^2$ for g , isolate the variable on one side by performing the basic algebraic operations as shown below

  $\begin{array}{c}s=\frac{1}{2}g{t}^2\\ 2\cdot s=2\cdot \frac{1}{2}g{t}^2\\ 2s=g{t}^2\\ \frac{2s}{t^2}=\frac{g{t}^2}{t^2}\\ \frac{2s}{t^2}=g\end{array}$

Thus, the required formula is $g=\frac{2s}{t^2}$ .