To determine the kinetic energy of a ball with a mass of [tex]\( 0.5 \text{ kg} \)[/tex] and a velocity of [tex]\( 10 \text{ m/s} \)[/tex], we will use the kinetic energy formula:
[tex]\[ KE = \frac{1}{2} m v^2 \][/tex]
Here's the step-by-step solution:
1. Identify the given values:
- Mass ([tex]\( m \)[/tex]) = [tex]\( 0.5 \text{ kg} \)[/tex]
- Velocity ([tex]\( v \)[/tex]) = [tex]\( 10 \text{ m/s} \)[/tex]
2. Substitute the given values into the kinetic energy formula:
[tex]\[ KE = \frac{1}{2} \times 0.5 \text{ kg} \times (10 \text{ m/s})^2 \][/tex]
3. Perform the operations inside the parentheses first:
[tex]\[ (10 \text{ m/s})^2 = 100 \text{ m}^2/\text{s}^2 \][/tex]
4. Substitute this value back into the formula:
[tex]\[ KE = \frac{1}{2} \times 0.5 \text{ kg} \times 100 \text{ m}^2/\text{s}^2 \][/tex]
5. Multiply [tex]\( \frac{1}{2} \)[/tex] by [tex]\( 0.5 \text{ kg} \)[/tex]:
[tex]\[ \frac{1}{2} \times 0.5 \text{ kg} = 0.25 \text{ kg} \][/tex]
6. Multiply the result by [tex]\( 100 \text{ m}^2/\text{s}^2 \)[/tex]:
[tex]\[ 0.25 \text{ kg} \times 100 \text{ m}^2/\text{s}^2 = 25 \text{ J} \][/tex]
Therefore, the kinetic energy of the ball is [tex]\( 25 \text{ J} \)[/tex], so the correct answer is:
[tex]\[ \boxed{25 \text{ J}} \][/tex]
