Solve for v0 s(t)=1/2gt^2+v_0t+s_0

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

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.

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

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

Simplify the left side.

Cancel the common factor of $t$ .

Cancel the common factor.

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

Divide $s$ by $1$ .

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

Simplify the right side.

Simplify each term.

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

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

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

Cancel the common factors.

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

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

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

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

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

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

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

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

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

Cancel the common factor of $t$ .

Cancel the common factor.

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

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

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