A car accelerates uniformly from rest to a speed of 6.58 m/s in 6.5 seconds.  Find the distance the car travels during this time. **Round your answer to the nearest whole number.**

To find the distance the car travels during the acceleration, we can use the following kinematic equation:

\[
d = v_i t + \frac{1}{2}at^2
\]

Since the car starts from rest, the initial velocity \(v_i\) is 0, simplifying the equation to:

\[
d = \frac{1}{2}at^2
\]

First, we need to find the acceleration \(a\), using the formula:

\[
a = \frac{v_f - v_i}{t}
\]

Here:
- \(v_i = 0 \, \text{m/s}\) (initial velocity, since the car starts from rest)
- \(v_f = 6.58 \, \text{m/s}\) (final velocity)
- \(t = 6.5 \, \text{seconds}\) (time)

Substituting the values:

\[
a = \frac{6.58 \, \text{m/s} - 0 \, \text{m/s}}{6.5 \, \text{seconds}} = \frac{6.58 \, \text{m/s}}{6.5 \, \text{seconds}} \approx 1.012 \, \text{m/s}^2
\]

Now, substituting \(a\) and \(t\) into the displacement equation:

\[
d = \frac{1}{2} \times 1.012 \, \text{m/s}^2 \times (6.5 \, \text{seconds})^2
\]

\[
d = 0.506 \, \text{m/s}^2 \times 42.25 \, \text{seconds}^2
\]

\[
d \approx 21.39 \, \text{meters}
\]

Rounding to the nearest whole number, the car travels **21 meters** during this time.

Would you like further details or have any questions?

Here are some related questions you might consider:
1. What would the distance be if the car accelerated for 10 seconds?
2. How much time would it take to reach 10 m/s with the same acceleration?
3. What is the car’s average velocity during the acceleration?
4. How would the distance change if the final speed was 10 m/s?
5. Can you determine the acceleration if the car reached 20 meters in 6.5 seconds?

**Tip:** When rounding off your answer, ensure that all intermediate steps maintain sufficient decimal places to avoid errors in the final result.

Learn how to calculate the distance traveled by a car that accelerates uniformly from rest to a speed of 6.58 m/s in 6.5 seconds. Use the kinematic equations and formulas for uniform acceleration to find the solution. Suitable for Grades 9-10 students studying physics.

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