Train at constant speed

Problem

Uniform motion. A train travels at a constant $120\;\text{km/h}$. How long does it take to cover $30\;\text{km}$?

Solution

The motion is uniform (constant speed), so time, distance and speed are linked by the relation:

$v = \frac{x}{t} \quad\Longrightarrow\quad t = \frac{x}{v}$

It is convenient to work in consistent units. Let us convert the speed into metres per second, recalling that $1\;\text{km/h} = \tfrac{1}{3{,}6}\;\text{m/s}$:

$v = \frac{120}{3{,}6} \approx 33{,}3\;\mathrm{m/s}$

The distance is $x = 30\;\text{km} = 30\,000\;\text{m}$. Substituting:

$t = \frac{30\,000}{33{,}3} = 900\;\mathrm{s}$

Which corresponds to $900\;\text{s} = 15\;\text{min}$. (The same result is reached more quickly by staying in km and hours: $t = 30/120 = 0{,}25\;\text{h} = 15\;\text{min}$.)

$\ev{t = 900\;\mathrm{s} = 15\;\mathrm{min}}$

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Topics: Cinematica Concepts: Velocità media