To find 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 can use the given formula for kinetic energy:
[tex]\[ KE = \frac{1}{2} m v^2 \][/tex]
Here are the step-by-step details on how to solve it:
1. Identify the given values:
- Mass, [tex]\( m = 0.5 \, \text{kg} \)[/tex]
- Velocity, [tex]\( v = 10 \, \text{m/s} \)[/tex]
2. Plug these values into the kinetic energy formula:
[tex]\[ KE = \frac{1}{2} \times 0.5 \, \text{kg} \times (10 \, \text{m/s})^2 \][/tex]
3. Calculate the velocity squared:
[tex]\[ (10 \, \text{m/s})^2 = 100 \, \text{m}^2/\text{s}^2 \][/tex]
4. Substitute this back into the equation:
[tex]\[ KE = \frac{1}{2} \times 0.5 \, \text{kg} \times 100 \, \text{m}^2/\text{s}^2 \][/tex]
5. Multiply the constants:
[tex]\[ KE = \frac{1}{2} \times 0.5 \times 100 \][/tex]
6. Simplify the multiplication:
[tex]\[ KE = 0.25 \times 100 \][/tex]
7. Calculate the final result:
[tex]\[ KE = 25 \, \text{J} \][/tex]
Thus, the kinetic energy of the ball is [tex]\( 25 \, \text{J} \)[/tex].
So, the correct answer is:
[tex]\[ \boxed{25 \, \text{J}} \][/tex]
