Solve for a S=ut+1/2at^2

$S = u t + \frac{1}{2} a t^{2}$

Rewrite the equation as $u t + \frac{1}{2} \cdot (a t^{2}) = S$ .

$u t + \frac{1}{2} \cdot (a t^{2}) = S$

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

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

$u t + \frac{a}{2} t^{2} = S$

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

$u t + \frac{a t^{2}}{2} = S$

Subtract $u t$ from both sides of the equation.

$\frac{a t^{2}}{2} = S - u t$

Multiply both sides of the equation by $2$ .

$2 \frac{a t^{2}}{2} = 2 (S - u t)$

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$2 \frac{a t^{2}}{2} = 2 (S - u t)$

Rewrite the expression.

$a t^{2} = 2 (S - u t)$

Simplify the right side.

Simplify $2 (S - u t)$ .

Apply the distributive property.

$a t^{2} = 2 S + 2 (- u t)$

Multiply $- 1$ by $2$ .

$a t^{2} = 2 S - 2 u t$

Divide each term in $a t^{2} = 2 S - 2 u t$ by $t^{2}$ and simplify.

Divide each term in $a t^{2} = 2 S - 2 u t$ by $t^{2}$ .

$\frac{a t^{2}}{t^{2}} = \frac{2 S}{t^{2}} + \frac{- 2 u t}{t^{2}}$

Simplify the left side.

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

Cancel the common factor.

$\frac{a t^{2}}{t^{2}} = \frac{2 S}{t^{2}} + \frac{- 2 u t}{t^{2}}$

Divide $a$ by $1$ .

$a = \frac{2 S}{t^{2}} + \frac{- 2 u t}{t^{2}}$

Simplify the right side.

Simplify each term.

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

Factor $t$ out of $- 2 u t$ .

$a = \frac{2 S}{t^{2}} + \frac{t (- 2 u)}{t^{2}}$

Cancel the common factors.

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

$a = \frac{2 S}{t^{2}} + \frac{t (- 2 u)}{t \cdot t}$

Cancel the common factor.

$a = \frac{2 S}{t^{2}} + \frac{t (- 2 u)}{t \cdot t}$

Rewrite the expression.

$a = \frac{2 S}{t^{2}} + \frac{- 2 u}{t}$

Move the negative in front of the fraction.

$a = \frac{2 S}{t^{2}} - \frac{2 u}{t}$

Solve for a S=ut+1/2at^2

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