Kinematics — 1D Motion, Graphs & Relative Velocity (Medium)

Quick Recap — 1D Motion, Graphs & Relative Velocity

• Equations (constant $a$): $v=u+at$, $s=ut+\tfrac12 at^2$, $v^2=u^2+2as$; distance in the $n$-th second $s_n=u+a\!\left(n-\tfrac12\right)$.
• Free fall ($g=10$): $h=\tfrac12 gt^2$; thrown up with speed $u$: max height $\dfrac{u^2}{2g}$, time up $\dfrac{u}{g}$, total flight $\dfrac{2u}{g}$.
• Graphs: slope of $x$–$t$ is velocity; slope of $v$–$t$ is acceleration; area under $v$–$t$ is displacement, under $a$–$t$ is change in velocity.
• Relative velocity: $\vec v_{AB}=\vec v_A-\vec v_B$ (subtract for same direction, add for opposite).

Worked mini-example. A body starts from rest with $a=2$ m/s$^2$. After 5 s: $v=at=10$ m/s and $s=\tfrac12 at^2=25$ m.