An airplane accelerates from a velocity of 27.38 m/s at a constant rate of 2.81 m/s2 over 545.49 m. What is its final velocity?

To find the final velocity of the airplane, we can use the 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 (\( 27.38 \, \text{m/s} \)),
- \( a \) is the acceleration (\( 2.81 \, \text{m/s}^2 \)),
- \( d \) is the displacement (\( 545.49 \, \text{m} \)).

We can solve for \( v_f \):

\[
v_f = \sqrt{v_i^2 + 2ad}
\]

Let's plug in the values and calculate the final velocity.import math

# Given values
v_i = 27.38  # initial velocity in m/s
a = 2.81  # acceleration in m/s^2
d = 545.49  # displacement in meters

# Using the equation for final velocity: v_f = sqrt(v_i^2 + 2ad)
v_f = math.sqrt(v_i**2 + 2 * a * d)
v_fThe final velocity of the airplane after accelerating over 545.49 meters is approximately \( 61.77 \, \text{m/s} \).

Do you have any questions or would you like more details?

Here are 5 related questions:
1. How long does it take for the airplane to cover the 545.49 meters?
2. How would the final velocity change if the initial velocity was 0 m/s?
3. What is the airplane's average velocity during this period?
4. How far would the airplane travel if it accelerated for 20 seconds instead?
5. What would happen to the final velocity if the acceleration increased to 5 m/s²?

**Tip:** In problems involving motion, it's helpful to know which kinematic equation to use based on the given information and the unknowns you need to solve for.

Learn how to calculate the final velocity of an airplane accelerating from 27.38 m/s at a constant rate of 2.81 m/s² over a distance of 545.49 meters. This problem involves kinematic equations of motion, suitable for Grades 10-12 students.

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