Question

1. what is the mass of an object that has 324 j of ke when moving at 9 m/s? 13. a 10 kg mass has a ke of 125 j what is its velocity?

Explanation:

Step1: Recall the kinetic energy formula

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

Step2: Solve for mass in the first problem

Given $KE = 324\ J$ and $v=9\ m/s$. Rearrange the formula to solve for $m$: $m=\frac{2KE}{v^{2}}$.
Substitute the values: $m=\frac{2\times324}{9^{2}}=\frac{648}{81}=8\ kg$.

Step3: Solve for velocity in the second problem

Given $m = 10\ kg$ and $KE=125\ J$. Rearrange the formula $KE=\frac{1}{2}mv^{2}$ to solve for $v$: $v=\sqrt{\frac{2KE}{m}}$.
Substitute the values: $v=\sqrt{\frac{2\times125}{10}}=\sqrt{\frac{250}{10}}=\sqrt{25}=5\ m/s$.

Answer:

1. The mass is $8\ kg$.
2. The velocity is $5\ m/s$.