Calculating Uniform Acceleration
2 guided lessons · 18 checks · 1. Forces & Motion → Movement & Position
Guided lessons for this note
Which concept don't you understand yet?
We'll explain it simply and check your understanding. Pick any lesson — any order works.
0 of 18 checks correct so far
Lesson 1 of 2
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.
Choose a confidence level to continue.
Prefer to read it all at once? Show the full lesson as a page
1.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.
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.
First pass
Square the finishing speed; it equals the square of the starting speed plus two times the acceleration times the distance covered. Use it whenever time never enters the question.
Analogy — It is a four-piece jigsaw: name any three pieces (two speeds, the acceleration, or the distance) and the equation hands you the fourth.
Exam pointer — Start every answer by listing the known quantities with their symbols; a labelled list earns credit and points straight at the right equation.
Going deeper
The squares are the price of excluding time: v² = u² + 2as is the time-free combination of the velocity-change relationship with the distance covered under constant acceleration.
Analogy — Where a = Δv/t needs a clock, this equation is the shortcut that survives with only the speedometer and the odometer.
Exam pointer — Watch 'from rest': it pins u = 0 and quietly removes one term from the squares before any arithmetic starts.
Checks
0 of 9 attempted · 0 correct
2.Rearranging without a triangle
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.
Key points
- Anything done to the equation must be done to both sides, and each operation is undone by its opposite.
- To isolate s: subtract u² from both sides, then divide both sides by 2a, giving s = (v² − u²) / (2a).
- Squaring is undone by square-rooting, multiplication by division, subtraction by addition.
- Showing the rearrangement earns method marks; the worked case gives s = (16² − 0²) / (2 × 2.5) = 256 / 5 = 51.2 m, quoted as 51 m to two significant figures.
- Solving for the acceleration works the same when an object uniformly slows: a = (v² − u²) / (2s) comes out negative, and that negative is the deceleration.
First pass
To find the distance, first peel the u² off with subtraction, then peel the 2a off with division. What remains on the other side is the answer: v² minus u², all over 2a.
Analogy — Undoing an equation is like unwrapping a parcel: remove the outermost layer (the division by 2a) last, and the same cut must go through every layer at once.
Exam pointer — Write the rearranged line (s = (v² − u²)/(2a)) before substituting numbers; that single line is usually a method mark.
Going deeper
The rearrangement order mirrors the equation's construction: 2as was added to u², so subtract u² first; s is multiplied by 2a, so divide last. Each inverse lands on both sides simultaneously.
Analogy — Algebraic undressing follows the reverse of dressing: last on, first off, applied everywhere at once.
Exam pointer — Keep the subtraction order v² − u²; flipping it to u² − v² flips the sign of the whole numerator and, with it, the physics.
Checks
0 of 9 attempted · 0 correct
Guided content from the SME authoring corpus — note rn_ZgGMNrRGBKvYxxFf, pinned at aa6485187429 · promoted SyllabAI/syllabai-resources b3caaaa90c5e