$$\text{Speed} = \frac{\text{distance}}{\text{time}} \qquad \text{Velocity} = \frac{\text{displacement}}{\text{time}} \qquad a = \frac{v - u}{t}$$

Equations of uniformly accelerated motion

$$v = u + at \qquad s = ut + \tfrac{1}{2}at^2 \qquad v^2 = u^2 + 2as \qquad s = \frac{u + v}{2}\,t$$ $u$ = initial velocity, $v$ = final velocity, $a$ = acceleration, $t$ = time, $s$ = displacement.

Free fall (take $a = g$)

$$v = gt \qquad h = \tfrac{1}{2}gt^2 \qquad v^2 = 2gh$$ Going up: $a = -g$; at the highest point $v = 0$. Time to the top $= \dfrac{u}{g}$, maximum height $= \dfrac{u^2}{2g}$.

Graphs

• Displacement-time graph: gradient $=$ velocity.
• Velocity-time graph: gradient $=$ acceleration; area under the graph $=$ displacement.

Projectiles (launched at speed $u$ and angle $\theta$)

$$\text{Time of flight} = \frac{2u\sin\theta}{g} \qquad \text{Range} = \frac{u^2\sin 2\theta}{g} \qquad \text{Max height} = \frac{u^2\sin^2\theta}{2g}$$