the equation $k = \\frac{1}{2}mv^{2}$ represents the energy an object has based on its motion. the kinetic…

the equation $k = \\frac{1}{2}mv^{2}$ represents the energy an object has based on its motion. the kinetic energy, $k$, is based on the mass of the object, $m$, and the velocity of the object, $v$. lashandra is given $k$ and $v$ for 10 different objects. in order to make solving more efficient, she solves the equation for $m$: $m = \\frac{k}{2v^{2}}$. after attempting to determine the mass of a few objects, lashandra realizes there must be something wrong with her formula. what is lashandras error? she should have multiplied by 2 instead of dividing by 2. she should have multiplied by $\\frac{1}{2}$ instead of dividing by 2. she should have used the square root to move the squared term to the other side of the equation. she should have squared the $k$ when moving the $v^{2}$ to the other side of the equation.

the equation $k = \\frac{1}{2}mv^{2}$ represents the energy an object has based on its motion. the kinetic energy, $k$, is based on the mass of the object, $m$, and the velocity of the object, $v$. lashandra is given $k$ and $v$ for 10 different objects. in order to make solving more efficient, she solves the equation for $m$: $m = \\frac{k}{2v^{2}}$. after attempting to determine the mass of a few objects, lashandra realizes there must be something wrong with her formula. what is lashandras error? she should have multiplied by 2 instead of dividing by 2. she should have multiplied by $\\frac{1}{2}$ instead of dividing by 2. she should have used the square root to move the squared term to the other side of the equation. she should have squared the $k$ when moving the $v^{2}$ to the other side of the equation.

Answer

Explanation:

Step1: Start with the kinetic - energy formula

The kinetic - energy formula is $K=\frac{1}{2}mv^{2}$.

Step2: Solve for $m$

Multiply both sides of the equation by $2$ to get $2K = mv^{2}$. Then divide both sides by $v^{2}$ to isolate $m$. So, $m=\frac{2K}{v^{2}}$.

Step3: Analyze Lashandra's work

Lashandra got $m=\frac{K}{2v^{2}}$. Her error is that she should have multiplied by $2$ instead of dividing by $2$ when solving for $m$ from $K=\frac{1}{2}mv^{2}$.

Answer:

She should have multiplied by 2 instead of dividing by 2.