Solve for v d=vt-1/2at^2

$d = v t - \frac{1}{2} a t^{2}$

Step 1

Rewrite the equation as $v t - \frac{1}{2} \cdot (a t^{2}) = d$ .

$v t - \frac{1}{2} \cdot (a t^{2}) = d$

Step 2

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

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

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

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

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

Step 3

Add $\frac{t^{2} a}{2}$ to both sides of the equation.

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

Step 4

Divide each term in $v t = d + \frac{t^{2} a}{2}$ by $t$ and simplify.

Divide each term in $v t = d + \frac{t^{2} a}{2}$ by $t$ .

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

Simplify the left side.

Cancel the common factor of $t$ .

Cancel the common factor.

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

Divide $v$ by $1$ .

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

Simplify the right side.

Simplify each term.

Multiply the numerator by the reciprocal of the denominator.

$v = \frac{d}{t} + \frac{t^{2} a}{2} \cdot \frac{1}{t}$

Combine.

$v = \frac{d}{t} + \frac{t^{2} a \cdot 1}{2 t}$

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

Factor $t$ out of $t^{2} a \cdot 1$ .

$v = \frac{d}{t} + \frac{t (t a \cdot 1)}{2 t}$

Cancel the common factors.

Factor $t$ out of $2 t$ .

$v = \frac{d}{t} + \frac{t (t a \cdot 1)}{t \cdot 2}$

Cancel the common factor.

$v = \frac{d}{t} + \frac{t (t a \cdot 1)}{t \cdot 2}$

Rewrite the expression.

$v = \frac{d}{t} + \frac{t a \cdot 1}{2}$

Multiply $t$ by $1$ .

$v = \frac{d}{t} + \frac{a t}{2}$