if all else is constant, which would cause the greatest increase in kinetic energy of a moving object? mass…

if all else is constant, which would cause the greatest increase in kinetic energy of a moving object? mass and velocity are each reduced by one - half. mass is reduced by one - half, and velocity is doubled. mass is doubled, and velocity is reduced by one - half. mass and velocity are each doubled.

if all else is constant, which would cause the greatest increase in kinetic energy of a moving object? mass and velocity are each reduced by one - half. mass is reduced by one - half, and velocity is doubled. mass is doubled, and velocity is reduced by one - half. mass and velocity are each doubled.

Answer

Answer:

D. Mass and velocity are each doubled.

Explanation:

Step1: Recall kinetic - energy formula

The formula for kinetic energy is $K = \frac{1}{2}mv^{2}$, where $m$ is mass and $v$ is velocity.

Step2: Analyze Option A

If $m$ becomes $\frac{m}{2}$ and $v$ becomes $\frac{v}{2}$, then $K_{A}=\frac{1}{2}(\frac{m}{2})(\frac{v}{2})^{2}=\frac{1}{2}\times\frac{m}{2}\times\frac{v^{2}}{4}=\frac{1}{16}mv^{2}$. The new kinetic - energy is $\frac{1}{8}$ of the original.

Step3: Analyze Option B

If $m$ becomes $\frac{m}{2}$ and $v$ becomes $2v$, then $K_{B}=\frac{1}{2}(\frac{m}{2})(2v)^{2}=\frac{1}{2}\times\frac{m}{2}\times4v^{2}=mv^{2}$. The new kinetic - energy is 2 times the original.

Step4: Analyze Option C

If $m$ becomes $2m$ and $v$ becomes $\frac{v}{2}$, then $K_{C}=\frac{1}{2}(2m)(\frac{v}{2})^{2}=\frac{1}{2}\times2m\times\frac{v^{2}}{4}=\frac{1}{4}mv^{2}$. The new kinetic - energy is $\frac{1}{2}$ of the original.

Step5: Analyze Option D

If $m$ becomes $2m$ and $v$ becomes $2v$, then $K_{D}=\frac{1}{2}(2m)(2v)^{2}=\frac{1}{2}\times2m\times4v^{2}=4mv^{2}$. The new kinetic - energy is 8 times the original. So, doubling both mass and velocity causes the greatest increase in kinetic energy.