Uniform acceleration, free fall and projectiles

Last time

Before we start: last time, in SI units, prefixes and homogeneity, you learned these points. Here they are again on one card. Keep them in mind, because today builds on them.

Two balls, one drop

Drop one ball, and at the same moment throw another sideways. Which hits the floor first? Both hit together. The sideways ball moves across at a steady speed, but downwards it does exactly the same as the dropped ball. That idea runs through this whole lesson.

The four equations

They apply only when the acceleration is constant. The symbols are s displacement, u initial velocity, v final velocity, a acceleration and t time. First: final velocity equals initial velocity plus acceleration times time. Second: displacement equals initial velocity times time, plus a half a t squared. Third: v squared equals u squared plus two a s. Fourth: s equals a half of u plus v, times t.

Where they come from

Acceleration is change in velocity over time: a equals v minus u over t. Rearrange for v equals u plus a t. The displacement is the area under the v–t graph: average velocity times time. Substitute v from the first equation: s equals u t plus a half a t squared.

Choosing the equation

Write down s, u, v, a and t. Mark the three you know and the one you want. The missing variable tells you the equation. No t needed? Use v squared equals u squared plus two a s. No v needed? Use s equals u t plus a half a t squared. No s needed? Use v equals u plus a t. Take one direction as positive, and give every vector its sign.