1. Understand the Concepts

* Uniform Acceleration: This means the plane's velocity changes at a constant rate.

* Displacement: The overall change in position of the plane.

* Initial Velocity (v₀): 59 m/s

* Final Velocity (v): 78 m/s

* Time (t): 12 s

2. Choose the Right Equation

We can use the following equation of motion for uniformly accelerated motion:

* d = v₀t + (1/2)at²

Where:

* d = displacement

* v₀ = initial velocity

* t = time

* a = acceleration

3. Calculate Acceleration (a)

First, we need to find the acceleration using the following equation:

* a = (v - v₀) / t

Substitute the given values:

* a = (78 m/s - 59 m/s) / 12 s

* a = 1.58 m/s²

4. Calculate Displacement (d)

Now, plug the values for v₀, t, and a into the equation for displacement:

* d = (59 m/s)(12 s) + (1/2)(1.58 m/s²)(12 s)²

* d = 708 m + 114.24 m

* d = 822.24 m

Answer: The displacement of the plane is approximately 822.24 meters.