To determine the kinetic energy of a ball with a mass of 0.5 kg and a velocity of 10 m/s, you can use the kinetic energy formula:
[tex]\[ KE = \frac{1}{2} mv^2 \][/tex]
where:
- [tex]\( KE \)[/tex] is the kinetic energy,
- [tex]\( m \)[/tex] is the mass of the object,
- [tex]\( v \)[/tex] is the velocity of the object.
Here is a detailed, step-by-step solution:
1. Identify the given values:
- Mass, [tex]\( m = 0.5 \)[/tex] kg
- Velocity, [tex]\( v = 10 \)[/tex] m/s
2. Plug these values into the kinetic energy formula:
[tex]\[ KE = \frac{1}{2} \times 0.5 \times (10)^2 \][/tex]
3. Calculate the velocity squared term first:
[tex]\[ (10)^2 = 100 \][/tex]
4. Multiply the mass by the squared velocity:
[tex]\[ 0.5 \times 100 = 50 \][/tex]
5. Lastly, multiply by [tex]\(\frac{1}{2}\)[/tex]:
[tex]\[ \frac{1}{2} \times 50 = 25 \][/tex]
Therefore, the kinetic energy of the ball is [tex]\(25 J\)[/tex].
The correct answer is [tex]\(25 J\)[/tex].
