3 (a) (i) An aircraft starts from rest and accelerates along the runway for 36s to reach take-off velocity - Edexcel - GCSE Physics Combined Science - Question 3 - 2022 - Paper 1

We can apply the equation of motion:
$v² = u² + 2ax$
Rearranging the formula to find distance (x):
$x = \frac{v² - u²}{2a}$
Substituting the known values:
$x = \frac{82² - 0²}{2 \times 2.28}$
Calculating gives:
$x = \frac{6724}{4.56} \approx 1470.4 ext{ m}$
Thus, the aircraft travels approximately 1470.4 meters before take-off.

One reason could be that real-life scenarios involve factors such as wind resistance and mechanical failures, which can affect the acceleration and distance requirements. Additionally, safety margins are included to ensure a safe take-off process.

The formula for kinetic energy (KE) is:
$KE = \frac{1}{2} mv²$
where:
m = mass of the aircraft (3.6 × 10² kg),
v = velocity (71 m/s).
Substituting the values into the equation:
$KE = \frac{1}{2} \times 3.6 \times 10² \times 71²$
Calculating gives:
$KE \approx 9.1 \times 10^5 \text{ J}$
So, the kinetic energy of the aircraft as it lands is approximately 9.1 × 10⁵ joules.

One way the energy has been transferred is through thermal dissipation due to air resistance and friction during landing.