Finite Math Examples

$s = \frac{1}{2} \cdot (g t^{2}) + v t$

Step 1

Rewrite the equation as $\frac{1}{2} \cdot (g t^{2}) + v t = s$ .

$\frac{1}{2} \cdot (g t^{2}) + v t = s$

Step 2

Multiply $\frac{1}{2} (g t^{2})$ .

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Step 2.1

Combine $g$ and $\frac{1}{2}$ .

$\frac{g}{2} t^{2} + v t = s$

Step 2.2

Combine $\frac{g}{2}$ and $t^{2}$ .

$\frac{g t^{2}}{2} + v t = s$

Step 3

Subtract $\frac{g t^{2}}{2}$ from both sides of the equation.

$v t = s - \frac{g t^{2}}{2}$

Step 4

Divide each term in $v t = s - \frac{g t^{2}}{2}$ by $t$ and simplify.

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Step 4.1

Divide each term in $v t = s - \frac{g t^{2}}{2}$ by $t$ .

$\frac{v t}{t} = \frac{s}{t} + \frac{- \frac{g t^{2}}{2}}{t}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $t$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{v t}{t} = \frac{s}{t} + \frac{- \frac{g t^{2}}{2}}{t}$

Step 4.2.1.2

Divide $v$ by $1$ .

$v = \frac{s}{t} + \frac{- \frac{g t^{2}}{2}}{t}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Simplify each term.

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Step 4.3.1.1

Multiply the numerator by the reciprocal of the denominator.

$v = \frac{s}{t} - \frac{g t^{2}}{2} \cdot \frac{1}{t}$

Step 4.3.1.2

Cancel the common factor of $t$ .

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Step 4.3.1.2.1

Move the leading negative in $- \frac{g t^{2}}{2}$ into the numerator.

$v = \frac{s}{t} + \frac{- g t^{2}}{2} \cdot \frac{1}{t}$

Step 4.3.1.2.2

Factor $t$ out of $- g t^{2}$ .

$v = \frac{s}{t} + \frac{t (- g t)}{2} \cdot \frac{1}{t}$

Step 4.3.1.2.3

Cancel the common factor.

$v = \frac{s}{t} + \frac{t (- g t)}{2} \cdot \frac{1}{t}$

Step 4.3.1.2.4

Rewrite the expression.

$v = \frac{s}{t} + \frac{- g t}{2}$

Step 4.3.1.3

Move the negative in front of the fraction.

$v = \frac{s}{t} - \frac{g t}{2}$