A 2 kg object moves with a velocity of 4 m/s for a time of 10 seconds. How much KE does the object possess? 1 Ex -my² 2 E = kinetic energy of object m = mass of object v = speed of object O 16 w O 16 J O8J O 8 W

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### Understanding Kinetic Energy 

**Problem Statement:**
A 2 kg object moves with a velocity of 4 m/s for a time of 10 seconds. How much kinetic energy (KE) does the object possess?

**Kinetic Energy Formula:**
\[ E_k = \frac{1}{2}mv^2 \]

Where:
- \( E_k \) = Kinetic energy of the object
- \( m \) = Mass of the object (in kilograms)
- \( v \) = Speed of the object (in meters per second)

**Given Data:**
- Mass \( m \) = 2 kg
- Velocity \( v \) = 4 m/s

To find the kinetic energy of the object, substitute the given values into the kinetic energy formula:

\[ E_k = \frac{1}{2} \times 2 \, \text{kg} \times (4 \, \text{m/s})^2 \]

First calculate the velocity squared:
\[ (4 \, \text{m/s})^2 = 16 \, \text{m}^2/\text{s}^2 \]

Then multiply by the mass and the factor \( \frac{1}{2} \):
\[ E_k = \frac{1}{2} \times 2 \, \text{kg} \times 16 \, \text{m}^2/\text{s}^2 \]
\[ E_k = 1 \times 16 \, \text{kg} \cdot \text{m}^2/\text{s}^2 \]
\[ E_k = 16 \, \text{J} \]

Therefore, the object possesses 16 Joules of kinetic energy.

**Answer Options:**
- 16 W
- **16 J**
- 8 J
- 8 W

**Explanation:**
The correct unit for kinetic energy is Joules (J), not Watts (W), which are units of power. Hence, the correct answer is: **16 J**.
Transcribed Image Text:### Understanding Kinetic Energy **Problem Statement:** A 2 kg object moves with a velocity of 4 m/s for a time of 10 seconds. How much kinetic energy (KE) does the object possess? **Kinetic Energy Formula:** \[ E_k = \frac{1}{2}mv^2 \] Where: - \( E_k \) = Kinetic energy of the object - \( m \) = Mass of the object (in kilograms) - \( v \) = Speed of the object (in meters per second) **Given Data:** - Mass \( m \) = 2 kg - Velocity \( v \) = 4 m/s To find the kinetic energy of the object, substitute the given values into the kinetic energy formula: \[ E_k = \frac{1}{2} \times 2 \, \text{kg} \times (4 \, \text{m/s})^2 \] First calculate the velocity squared: \[ (4 \, \text{m/s})^2 = 16 \, \text{m}^2/\text{s}^2 \] Then multiply by the mass and the factor \( \frac{1}{2} \): \[ E_k = \frac{1}{2} \times 2 \, \text{kg} \times 16 \, \text{m}^2/\text{s}^2 \] \[ E_k = 1 \times 16 \, \text{kg} \cdot \text{m}^2/\text{s}^2 \] \[ E_k = 16 \, \text{J} \] Therefore, the object possesses 16 Joules of kinetic energy. **Answer Options:** - 16 W - **16 J** - 8 J - 8 W **Explanation:** The correct unit for kinetic energy is Joules (J), not Watts (W), which are units of power. Hence, the correct answer is: **16 J**.
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