Solve for a d=v_0^t+(at^2)/2

$d = v_{0^{t}} + \frac{a t^{2}}{2}$

Step 1

Rewrite the equation as $v_{0^{t}} + \frac{a t^{2}}{2} = d$ .

$v_{0^{t}} + \frac{a t^{2}}{2} = d$

Step 2

Subtract $v_{0^{t}}$ from both sides of the equation.

$\frac{a t^{2}}{2} = d - v_{0^{t}}$

Step 3

Multiply both sides of the equation by $2$ .

$2 \frac{a t^{2}}{2} = 2 (d - v_{0^{t}})$

Step 4

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$2 \frac{a t^{2}}{2} = 2 (d - v_{0^{t}})$

Rewrite the expression.

$a t^{2} = 2 (d - v_{0^{t}})$

Simplify the right side.

Simplify $2 (d - v_{0^{t}})$ .

Apply the distributive property.

$a t^{2} = 2 d + 2 (- v_{0^{t}})$

Multiply $- 1$ by $2$ .

$a t^{2} = 2 d - 2 v_{0^{t}}$

Step 5

Divide each term in $a t^{2} = 2 d - 2 v_{0^{t}}$ by $t^{2}$ and simplify.

Divide each term in $a t^{2} = 2 d - 2 v_{0^{t}}$ by $t^{2}$ .

$\frac{a t^{2}}{t^{2}} = \frac{2 d}{t^{2}} + \frac{- 2 v_{0^{t}}}{t^{2}}$

Simplify the left side.

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

Cancel the common factor.

$\frac{a t^{2}}{t^{2}} = \frac{2 d}{t^{2}} + \frac{- 2 v_{0^{t}}}{t^{2}}$

Divide $a$ by $1$ .

$a = \frac{2 d}{t^{2}} + \frac{- 2 v_{0^{t}}}{t^{2}}$

Simplify the right side.

Move the negative in front of the fraction.

$a = \frac{2 d}{t^{2}} - \frac{2 v_{0^{t}}}{t^{2}}$