Solve for the indicated variable.
-$s = v t + \frac { 1 } { 2 } a t ^ { 2 } \quad$ for $t$
A) $t = \frac { v \pm \sqrt { v ^ { 2 } + 2 a s } } { 2 a }$
B) $t = \frac { - v \pm i \sqrt { v ^ { 2 } + 2 a s } } { a }$
C) $t = \frac { - v \pm \sqrt { v ^ { 2 } + 2 a s } } { a }$
D) $t = \frac { v \pm \sqrt { v ^ { 2 } + 2 a s } } { a }$

Question

Quizplus · Accepted Answer

To solve for $t$, we rearrange the equation $s = vt + \frac{1}{2}at^2$ into a standard quadratic form $at^2 + bt + c = 0$, where $a = \frac{1}{2}a$, $b = v$, and $c = -s$. Using the quadratic formula $t = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$, we substitute $a$, $b$, and $c$ with their respective values to get $t = \frac{-v \pm \sqrt{v^2 + 2as}}{a}$, which matches choice C.

Solve for the Indicated Variable s=vt+12at2s = v t + \frac { 1 } { 2 } a t ^ { 2 } \quads=vt+21​at2

Solve for the Indicated Variable $s = v t + \frac { 1 } { 2 } a t ^ { 2 } \quad$