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What is the kinetic energy of a ball with a mass of [tex][tex]$0.5 \, \text{kg}$[/tex][/tex] and a velocity of [tex][tex]$10 \, \text{m/s}$[/tex][/tex]?

(Formula: [tex][tex]$KE = \frac{1}{2} mv^2$[/tex][/tex])

A. [tex][tex]$25 \, \text{J}$[/tex][/tex]
B. [tex][tex]$5 \, \text{J}$[/tex][/tex]
C. [tex][tex]$50 \, \text{J}$[/tex][/tex]
D. [tex][tex]$100 \, \text{J}$[/tex][/tex]

Sagot :

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]