To find the final velocity of the plane, we can use the following kinematic equation:

$v_f^2 = v_i^2 + 2ad$

Where:

• $v_f$ is the final velocity (what we want to find),
• $v_i$ is the initial velocity (since it's not given, we'll assume it starts from rest, so $v_i = 0$),
• $a$ is the acceleration, which is 5 m/s²,
• $d$ is the distance traveled, which is 500 m.

Substituting the values into the equation:

$v_f^2 = 0 + 2(5)(500)$

$v_f^2 = 5000$

Now, take the square root of both sides:

$v_f = \sqrt{5000} \approx 70.71 \, \text{m/s}$

Thus, the final velocity attained by the plane is approximately $70.71 \, \text{m/s}$.

Would you like more details on this solution? Here are five related questions:

1. What if the plane had an initial velocity of 10 m/s? How would that change the final velocity?
2. How much time does it take for the plane to reach this final velocity?
3. What would the final velocity be if the distance traveled was 1000 meters?
4. How does the acceleration affect the final velocity?
5. Can you calculate the kinetic energy of the plane at the final velocity?

Tip: When solving kinematic problems, always check if you have enough information to apply the correct equation!