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The text for question 1 says:

"A car starts to accelerate at a rate of 3.20 m/s\(^2\) for 8.00 s until it finally slows to a stop. Calculate the distance traveled before it stopped."

### Step-by-Step Solution:

1. **Identify the given information:**
   - Acceleration, \(a = 3.20\) m/s\(^2\)
   - Time of acceleration, \(t = 8.00\) s
   - Initial velocity, \(v_0 = 0\) (assuming the car starts from rest)

2. **Determine the velocity of the car after accelerating for 8 seconds:**
   The final velocity \(v\) can be found using the formula for acceleration:

   \[
   v = v_0 + at
   \]

   Substituting the given values:

   \[
   v = 0 + (3.20 \, \text{m/s}^2)(8.00 \, \text{s}) = 25.6 \, \text{m/s}
   \]

   So, the car reaches a velocity of 25.6 m/s after accelerating for 8 seconds.

3. **Calculate the distance traveled during the acceleration:**
   The distance \(d_1\) traveled during this acceleration period can be calculated using the formula:

   \[
   d_1 = v_0 t + \frac{1}{2} a t^2
   \]

   Since the initial velocity \(v_0 = 0\), this simplifies to:

   \[
   d_1 = \frac{1}{2} \times 3.20 \, \text{m/s}^2 \times (8.00 \, \text{s})^2
   \]

   \[
   d_1 = \frac{1}{2} \times 3.20 \times 64
   \]

   \[
   d_1 = 102.4 \, \text{m}
   \]

   Thus, the distance traveled during acceleration is 102.4 meters.

### Final Answer:
- The car travels **102.4 meters** before it stops.

Would you like any more details on this solution or have any further questions?

### Related Questions:
1. What would be the distance traveled if the car accelerated at 4 m/s\(^2\) for the same time?
2. How much time would it take for the car to reach a velocity of 30 m/s with the same acceleration?
3. What would be the stopping distance if the car decelerated at a rate of 5 m/s\(^2\) from its final velocity?
4. How would the total distance change if the car continued to accelerate for an additional 5 seconds?
5. If the car had an initial velocity of 10 m/s, what would be the final velocity after 8 seconds of acceleration?

### Tip:
Remember that when working with constant acceleration, using kinematic equations helps simplify the process.

Learn how to calculate the distance traveled by a car accelerating at 3.20 m/s² for 8.00 s. This problem involves kinematic equations, acceleration calculations, and distance formulas. Suitable for high school students studying physics.

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