Part 1 · Motion on a straight line

Formula sheet

Everything for this part, in one place. Trains, boats, races and circular tracks are in part 2.

The relation, and its three faces


Speed	$s = \dfrac{d}{t}$
Distance	$d = s \times t$
Time	$t = \dfrac{d}{s}$
Units	$1 \text{ km/h} = \dfrac{5}{18}\text{ m/s}$ , and $1 \text{ m/s} = \dfrac{18}{5}\text{ km/h}$

When the distance is fixed — the most useful block on this page

Two bodies


Moving towards each other	relative speed $= s_1 + s_2$
Moving the same way	relative speed $= s_1 - s_2$
Time to meet, or to catch up	$\dfrac{\text{gap}}{\text{relative speed}}$

They start together, meet, and carry on — worth memorising


If they then need $t_1$ and $t_2$ more	$\dfrac{s_1}{s_2} = \sqrt{\dfrac{t_2}{t_1}}$
Time taken to reach the meeting point	$\sqrt{t_1 t_2}$

Average speed


Always	$\dfrac{\text{total distance}}{\text{total time}}$
Equal distances at $x$ and $y$	the harmonic mean, $\dfrac{2xy}{x+y}$
Equal times at $x$ and $y$	the arithmetic mean, $\dfrac{x+y}{2}$
Three equal distances	$\dfrac{3}{\frac{1}{x}+\frac{1}{y}+\frac{1}{z}}$
Never	the average of the speeds, unless the times are equal

Clocks