Potential and Kinetic Energy Worksheet - Free Printable

It looks like you've uploaded an image of a Kinetic Energy Practice Problems Answer Key, but the bottom part (problems 4 and 5) is blurred or partially obscured. However, I can help you solve Problem 4 and Problem 5 based on what's visible and standard physics principles.

Let’s go through each problem step by step and explain the solution.

---

🔷 Problem 4:

> What is the Kinetic Energy of a 1200 kg object that is moving with a speed of 24 m/s?

#### Step 1: Use the Kinetic Energy formula
$$
KE = \frac{1}{2}mv^2
$$

Where:
- $ m = 1200\,\text{kg} $
- $ v = 24\,\text{m/s} $

#### Step 2: Plug in values
$$
KE = \frac{1}{2}(1200\,\text{kg})(24\,\text{m/s})^2
$$
$$
KE = 600 \times (576)
$$
$$
KE = 345,600\,\text{J}
$$

✔ Answer:
$$
\boxed{KE = 345,600\,\text{J}} \quad \text{(or } 3.456 \times 10^5\,\text{J)}
$$

---

🔷 Problem 5:

> An object has a kinetic energy of 90 J and a mass of 15 kg. How fast is the object moving?

We are given:
- $ KE = 90\,\text{J} $
- $ m = 15\,\text{kg} $
- $ v = ? $

Use the same formula:
$$
KE = \frac{1}{2}mv^2
$$

Solve for $ v $:
$$
v^2 = \frac{2KE}{m}
$$
$$
v^2 = \frac{2 \times 90}{15} = \frac{180}{15} = 12
$$
$$
v = \sqrt{12} \approx 3.46\,\text{m/s}
$$

✔ Answer:
$$
\boxed{v \approx 3.46\,\text{m/s}}
$$

---

✔ Summary of Solutions:

| Problem | Given | Asked | Solution |
|--------|-------|-------|---------|
| 4 | $ m = 1200\,\text{kg}, v = 24\,\text{m/s} $ | $ KE = ? $ | $ KE = 345,600\,\text{J} $ |
| 5 | $ KE = 90\,\text{J}, m = 15\,\text{kg} $ | $ v = ? $ | $ v \approx 3.46\,\text{m/s} $ |

---

📌 Explanation of the Formula:

The kinetic energy of an object depends on its mass and the square of its velocity:
$$
KE = \frac{1}{2}mv^2
$$
This means:
- Doubling the mass doubles the kinetic energy.
- Doubling the speed quadruples the kinetic energy (since it's squared).

So even small changes in speed have large effects on kinetic energy!

---

If you'd like me to clarify any part or provide more examples, let me know!