SUVAT v² Equation — Runway Length Needed (Worked Example)

Medium

Problem

A light aircraft must reach 80 m/s to lift off and can accelerate at 2.5 m/s² along the runway. What minimum runway length does it need (starting from rest)?

Given

u = 0 m/s
v = 80 m/s
a = 2.5 m/s²

Find

The required distance s.

Principle

Rearranging v² = u² + 2as gives s directly from the speed requirement — no need to find the time first.

Formula

v^2 = u^2 + 2as

v² = u² + 2as

Solution

Rearrange: $s = \frac{v^2 - u^2}{2a}$
Substitute: $s = \frac{80^2 - 0}{2(2.5)}$
Calculate: $s = \frac{6400}{5} = 1280\ \mathrm{m}$

1280 m

Unit check

(m/s)² ÷ (m/s²) = m — a length, correct.

What this means physically

1280 m of runway just to reach flying speed — small airports need every metre, and on hot days (thinner air) the requirement grows further.

Common mistake

Solving for time first and rounding it, then computing distance — the rounding error compounds. Solve for s directly.