Answer :
To find the velocity of an object with a given mass and kinetic energy, we can use the formula for kinetic energy in terms of mass and velocity:
[tex]\[ KE = \frac{1}{2}mv^2 \][/tex]
Rearranging the formula to solve for velocity, \( v \), we get:
[tex]\[ v = \sqrt{\frac{2KE}{m}} \][/tex]
Given:
- Mass (\( m \)) = 11 kilograms
- Kinetic Energy (\( KE \)) = 792 joules
Plugging these values into the formula:
[tex]\[ v = \sqrt{\frac{2 \times 792 \, \text{J}}{11 \, \text{kg}}} \][/tex]
[tex]\[ v = \sqrt{\frac{1584 \, \text{J}}{11 \, \text{kg}}} \][/tex]
[tex]\[ v = \sqrt{144 \, \text{m}^2/\text{s}^2} \][/tex]
[tex]\[ v = 12 \, \text{m/s} \][/tex]
Therefore, the velocity of the object is \( 12 \, \text{m/s} \).
The correct answer is:
E. [tex]\( 12 \, \text{m/s} \)[/tex]
[tex]\[ KE = \frac{1}{2}mv^2 \][/tex]
Rearranging the formula to solve for velocity, \( v \), we get:
[tex]\[ v = \sqrt{\frac{2KE}{m}} \][/tex]
Given:
- Mass (\( m \)) = 11 kilograms
- Kinetic Energy (\( KE \)) = 792 joules
Plugging these values into the formula:
[tex]\[ v = \sqrt{\frac{2 \times 792 \, \text{J}}{11 \, \text{kg}}} \][/tex]
[tex]\[ v = \sqrt{\frac{1584 \, \text{J}}{11 \, \text{kg}}} \][/tex]
[tex]\[ v = \sqrt{144 \, \text{m}^2/\text{s}^2} \][/tex]
[tex]\[ v = 12 \, \text{m/s} \][/tex]
Therefore, the velocity of the object is \( 12 \, \text{m/s} \).
The correct answer is:
E. [tex]\( 12 \, \text{m/s} \)[/tex]
