SUVAT Displacement — Aircraft Takeoff Roll (Worked Example)

Medium

Problem

A passenger jet begins its takeoff roll from rest and accelerates uniformly at 2.5 m/s² for 30 s before lifting off. What length of runway does it use?

Given

u = 0 m/s
a = 2.5 m/s²
t = 30 s

Find

The takeoff distance s.

Principle

The displacement equation s = ut + ½at² gives distance directly from acceleration and time, without needing the liftoff speed first.

Formula

s = ut + \frac{1}{2}at^2

s = ut + ½at²

Solution

Write the equation: $s = ut + \frac{1}{2}at^2$
Starting from rest, $s = \frac{1}{2}(2.5)(30)^2$
Calculate: $s = 0.5 \times 2.5 \times 900$
Result: $s = 1125\ \mathrm{m}$

1125 m

Unit check

m/s² × s² = m. A length — correct.

What this means physically

1125 m of runway — typical for a medium jet, which is why runways are 2–4 km long: the plane needs margin for aborted takeoffs at even higher speeds.

Common mistake

Forgetting to square the time. The ½at² term grows quadratically — doubling the time quadruples this part of the distance.