To find the kinetic energy of a ball with a given mass and velocity, you can use the formula for kinetic energy:
[tex]\[ KE = \frac{1}{2} mv^2 \][/tex]
Here, [tex]\( m \)[/tex] represents the mass of the object and [tex]\( v \)[/tex] represents its velocity. Let's apply the given values:
- Mass ([tex]\( m \)[/tex]) = 0.5 kg
- Velocity ([tex]\( v \)[/tex]) = 10 m/s
Now substitute these values into the formula:
[tex]\[ KE = \frac{1}{2} \times 0.5 \, \text{kg} \times (10 \, \text{m/s})^2 \][/tex]
First, calculate the square of the velocity:
[tex]\[ (10 \, \text{m/s})^2 = 100 \, \text{m}^2/\text{s}^2 \][/tex]
Then, multiply this by the mass:
[tex]\[ 0.5 \, \text{kg} \times 100 \, \text{m}^2/\text{s}^2 = 50 \, \text{kg} \cdot \text{m}^2/\text{s}^2 \][/tex]
Finally, multiply by [tex]\( \frac{1}{2} \)[/tex]:
[tex]\[ KE = \frac{1}{2} \times 50 \, \text{J} = 25 \, \text{J} \][/tex]
Therefore, the kinetic energy of the ball is [tex]\( 25 \, \text{J} \)[/tex]. The correct answer is:
25 J
