The kinetic energy \( KE \) of an object can be calculated using the formula:
\[ KE = \frac{1}{2} m v^2 \]
where \( m \) is the mass of the object and \( v \) is its velocity.
Let's calculate the kinetic energy for each object.
Object 1:
- Mass \( m = 20 \) kg
- Velocity \( v = 4 \) m/s
\[ KE_1 = \frac{1}{2} \times 20 \times (4)^2 = \frac{1}{2} \times 20 \times 16 = 10 \times 16 = 160 , \text{J} \]
Object 2:
- Mass \( m = 6 \) kg
- Velocity \( v = 10 \) m/s
\[ KE_2 = \frac{1}{2} \times 6 \times (10)^2 = \frac{1}{2} \times 6 \times 100 = 3 \times 100 = 300 , \text{J} \]
Object 3:
- Mass \( m = 50 \) kg
- Velocity \( v = 2 \) m/s
\[ KE_3 = \frac{1}{2} \times 50 \times (2)^2 = \frac{1}{2} \times 50 \times 4 = 25 \times 4 = 100 , \text{J} \]
Object 4:
- Mass \( m = 10 \) kg
- Velocity \( v = 5 \) m/s
\[ KE_4 = \frac{1}{2} \times 10 \times (5)^2 = \frac{1}{2} \times 10 \times 25 = 5 \times 25 = 125 , \text{J} \]
Now let's summarize the kinetic energies:
- \( KE_1 = 160 , \text{J} \)
- \( KE_2 = 300 , \text{J} \)
- \( KE_3 = 100 , \text{J} \)
- \( KE_4 = 125 , \text{J} \)
Conclusion: Object 2 has the highest amount of kinetic energy at 300 J.