Guided lesson

Calculating Uniform Acceleration

1.10

2 guided lessons · 18 checks · 1. Forces & Motion → Movement & Position

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The v² = u² + 2as relationship

Some journeys never tell you their duration — only the speeds at the ends and the acceleration between them. For those, the squared relationship steps in: it connects initial speed, final speed, acceleration and distance moved without ever mentioning time. This lesson pins the equation and the meaning of every letter in it.

What you know already

One equation of this topic refuses the formula triangle: v² = u² + 2as links four quantities and leaves time out entirely. This lesson states the relationship for uniform acceleration, maps every symbol to its unit, and then practises the plain-algebra rearranging that replaces the triangle.

Key points of understanding

Uniform acceleration means constant acceleration: the velocity changes by the same amount every second.
The relationship for uniform acceleration is v² = u² + 2as; each symbol carries a meaning: v the final speed, u the initial speed, a the acceleration and s the distance moved.
The symbols carry s = distance moved in metres, u and v = initial and final speed in m/s, and a = acceleration in m/s².
This equation is the tool when the time taken is not known and is not asked for; it is also the one relationship no cover-and-read triangle can encode.

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1.The v² = u² + 2as relationship

1.10

Key points

Uniform acceleration means constant acceleration: the velocity changes by the same amount every second.
The relationship for uniform acceleration is v² = u² + 2as; each symbol carries a meaning: v the final speed, u the initial speed, a the acceleration and s the distance moved.
The symbols carry s = distance moved in metres, u and v = initial and final speed in m/s, and a = acceleration in m/s².
This equation is the tool when the time taken is not known and is not asked for; it is also the one relationship no cover-and-read triangle can encode.

Guided content from the SME authoring corpus — note rn_ZgGMNrRGBKvYxxFf, pinned at aa6485187429 · promoted SyllabAI/syllabai-resources b3caaaa90c5e

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2.Rearranging without a triangle

1.10

With the triangle unavailable, rearranging falls back on two universal algebra rules: treat both sides identically, and undo operations in reverse. This lesson applies them to isolate s, then runs the full worked car calculation — from rest, at 2.5 m/s², up to 16 m/s — and reads the distance off the end.