Ranking the speeds of four cars

Problem

Ranking. Four cars travel along a straight line at constant speed. (A) Covers $120\;\mathrm{m}$ in $6\;\mathrm{s}$. (B) Covers $45\;\mathrm{m}$ in $3\;\mathrm{s}$. (C) Covers $200\;\mathrm{m}$ in $10\;\mathrm{s}$. (D) Covers $300\;\mathrm{m}$ in $12\;\mathrm{s}$. Rank the speeds from smallest to largest (use "$=$" in case of a tie).

Solution

Method. Since these are motions at constant speed, for each car it suffices to compute $v = \Delta s / \Delta t$; a direct comparison of the ratios avoids any ambiguity.

$v_A = \frac{120}{6} = 20\;\mathrm{m/s}, \qquad v_B = \frac{45}{3} = 15\;\mathrm{m/s}$

$v_C = \frac{200}{10} = 20\;\mathrm{m/s}, \qquad v_D = \frac{300}{12} = 25\;\mathrm{m/s}$

Comparison. Cars A and C have the same speed ($20\;\mathrm{m/s}$); B is the slowest ($15\;\mathrm{m/s}$) and D the fastest ($25\;\mathrm{m/s}$). Ranking from smallest to largest:

$\ev{B < A = C < D}$

Note: covering more metres does not mean being faster. D covers more distance than A, but what matters is how much distance per unit of time.

Links

Topics: Kinematics Concepts: Average speed Skills: Ranking reasoning