Algebra Examples

$s (t) = \frac{1}{2} g t^{2} + v_{0} t + s_{0}$

Step 1

Remove parentheses.

$s t = \frac{1}{2} \cdot g t^{2} + v_{0} t + s_{0}$

Step 2

Divide each term in $s t = \frac{1}{2} \cdot (g t^{2}) + v_{0} t + s_{0}$ by $t$ and simplify.

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Step 2.1

Divide each term in $s t = \frac{1}{2} \cdot (g t^{2}) + v_{0} t + s_{0}$ by $t$ .

$\frac{s t}{t} = \frac{\frac{1}{2} \cdot (g t^{2})}{t} + \frac{v_{0} t}{t} + \frac{s_{0}}{t}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $t$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{s t}{t} = \frac{\frac{1}{2} \cdot (g t^{2})}{t} + \frac{v_{0} t}{t} + \frac{s_{0}}{t}$

Step 2.2.1.2

Divide $s$ by $1$ .

$s = \frac{\frac{1}{2} \cdot (g t^{2})}{t} + \frac{v_{0} t}{t} + \frac{s_{0}}{t}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Simplify each term.

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Step 2.3.1.1

Cancel the common factor of $t^{2}$ and $t$ .

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Step 2.3.1.1.1

Factor $t$ out of $\frac{1}{2} \cdot (g t^{2})$ .

$s = \frac{t (\frac{1}{2} \cdot (g t))}{t} + \frac{v_{0} t}{t} + \frac{s_{0}}{t}$

Step 2.3.1.1.2

Cancel the common factors.

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Step 2.3.1.1.2.1

Raise $t$ to the power of $1$ .

$s = \frac{t (\frac{1}{2} \cdot (g t))}{t^{1}} + \frac{v_{0} t}{t} + \frac{s_{0}}{t}$

Step 2.3.1.1.2.2

Factor $t$ out of $t^{1}$ .

$s = \frac{t (\frac{1}{2} \cdot (g t))}{t \cdot 1} + \frac{v_{0} t}{t} + \frac{s_{0}}{t}$

Step 2.3.1.1.2.3

Cancel the common factor.

$s = \frac{t (\frac{1}{2} \cdot (g t))}{t \cdot 1} + \frac{v_{0} t}{t} + \frac{s_{0}}{t}$

Step 2.3.1.1.2.4

Rewrite the expression.

$s = \frac{\frac{1}{2} \cdot (g t)}{1} + \frac{v_{0} t}{t} + \frac{s_{0}}{t}$

Step 2.3.1.1.2.5

Divide $\frac{1}{2} \cdot (g t)$ by $1$ .

$s = \frac{1}{2} \cdot (g t) + \frac{v_{0} t}{t} + \frac{s_{0}}{t}$

Step 2.3.1.2

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

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Step 2.3.1.2.1

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

$s = \frac{g}{2} t + \frac{v_{0} t}{t} + \frac{s_{0}}{t}$

Step 2.3.1.2.2

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

$s = \frac{g t}{2} + \frac{v_{0} t}{t} + \frac{s_{0}}{t}$

Step 2.3.1.3

Cancel the common factor of $t$ .

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Step 2.3.1.3.1

Cancel the common factor.

$s = \frac{g t}{2} + \frac{v_{0} t}{t} + \frac{s_{0}}{t}$

Step 2.3.1.3.2

Divide $v_{0}$ by $1$ .

$s = \frac{g t}{2} + v_{0} + \frac{s_{0}}{t}$