SUVAT v² Equation — Dropped Object (Worked Example)

Easy

Problem

A wrench slips from a scaffold 20 m above the ground and falls from rest (ignore air resistance, g = 9.8 m/s²). With what speed does it hit the ground?

Given

u = 0 m/s
a = g = 9.8 m/s²
s = 20 m

Find

The impact speed v.

Principle

Free fall is constant-acceleration motion, so v² = u² + 2as applies with a = g and s the fall height.

Formula

v^2 = u^2 + 2as

v² = u² + 2as

Solution

Write the equation: $v^2 = u^2 + 2as$
Substitute: $v^2 = 0 + 2(9.8)(20)$
Calculate: $v^2 = 392$
Take the square root: $v = \sqrt{392} = 19.8\ \mathrm{m/s}$

19.8 m/s

Unit check

√(m/s² × m) = √(m²/s²) = m/s — a speed, correct.

What this means physically

19.8 m/s is about 71 km/h — a dropped wrench hits like a fast car crash, which is why hard hats are mandatory under scaffolds.

Common mistake

Taking the negative square root. Speed is the magnitude; the downward velocity would be −19.8 m/s in an upward-positive system, but the question asks for speed.