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Constant acceleration

Five equations hide in one trapezium.

Constant acceleration means a straight velocity–time line. Every suvat equation is just a different way of measuring that line — its gradient, its area, or the two combined. Nothing here needs memorising.

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The gradient

The line climbs from uu to vv over a time tt. Its gradient is the acceleration, so a=v−uta = \dfrac{v - u}{t}, which rearranges to the first equation.

v=u+atv = u + at

The area

The area under a velocity–time graph is the displacement. This area is a trapezium: two parallel sides uu and vv, a width tt.

s=12(u+v)ts = \tfrac12(u + v)t

Cut it in two

Slice the trapezium along the line v=uv = u. Below sits a rectangle u×tu \times t; above it a triangle of base tt and height v−u=atv - u = at, so area 12t×at\tfrac12 t \times at. Measuring down from the top instead gives s=vt−12at2s = vt - \tfrac12at^2.

s=ut+12at2s = ut + \tfrac12at^2

The fifth

The last equation is the only one with no picture of its own. Take the first two and eliminate tt — the difference of two squares does the rest.

v2=u2+2asv^2 = u^2 + 2as

Chapter 2

Five letters. Pick the equation missing the one you don't want.

Choosing between them, multi-stage journeys, vertical motion under gravity, and twelve graded exam questions with full worked solutions are waiting.