Question

analyzing work for errors
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 ).

lashandras equation

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 squared the ( k ) when moving the ( v^{2} ) to the other side of the equation.

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.

Explanation:

Step1: Solve the kinetic energy formula for \(m\)

Given \(K=\frac{1}{2}mv^{2}\). First, multiply both sides of the equation by \(2\) to get \(2K = mv^{2}\).

Step2: Isolate \(m\)

Then divide both sides by \(v^{2}\) to obtain \(m=\frac{2K}{v^{2}}\).

Answer:

She should have multiplied by \(2\) instead of dividing by \(2\).