運動学（等加速度運動）

Displacement $s$ is the directed distance from the start (unit m). Velocity $v$ is the rate of change of displacement (unit m/s) and is a vector — it carries direction. Acceleration $a$ is the rate of change of velocity (unit m/s${}^2$). All three use sign to show direction: once you choose a positive direction, anything pointing the opposite way is negative. Distance and speed are magnitudes only, but in Mechanics we work with the directed quantities — displacement, velocity and acceleration.

Four equations apply — but only when acceleration is constant. The symbols are $u$ (initial velocity), $v$ (final velocity), $a$ (acceleration), $t$ (time) and $s$ (displacement). The trick is to match the three quantities you are given against the one you want, then pick the equation that leaves out the quantity you neither know nor need. For instance, if time $t$ is neither given nor asked for, use $v^2=u^2+2as$.

An object thrown straight up or down moves with constant acceleration equal to gravity, $g$. In this course we use $g=10$ m/s${}^2$ unless told otherwise. Taking up as positive, gravity always acts downwards, so the acceleration is $a=-g=-10$ m/s${}^2$. The key fact for finding the greatest height is that at the top the velocity is momentarily zero ($v=0$). For an object that is simply falling, taking down as positive gives $a=+10$ m/s${}^2$ and keeps the signs simple.

A velocity–time ($v$–$t$) graph is full of information. The gradient of the graph gives the acceleration, and the area between the graph and the time axis gives the displacement. A straight sloping line means constant acceleration; a horizontal line means constant velocity (zero acceleration). Split the area into triangles, rectangles and trapezia and add them up to get the total distance travelled — no suvat needed.