Motion in One Dimension — Quick Summary

Mr Toogood's Physics · Mechanics

AQA 3.4.1.3
v = u + at
Missing: s
s = (u+v)/2 · t
Missing: a
s = ut + ½at²
Missing: v
v² = u² + 2as
Missing: t

Definitions

v = Δs/Δt  (velocity, vector)    a = Δv/Δt  (acceleration)

Speed (scalar) = rate of change of distance. Velocity (vector) = rate of change of displacement — must include a direction, and can be resolved into components.

QuantitySymbolUnits
Displacementsm
Initial velocityum s⁻¹
Final velocityvm s⁻¹
Accelerationam s⁻²
Timets

Choosing the right equation

Each SUVAT equation is missing exactly one of the five quantities (see the strip above). Method:

  1. Write down every quantity given, using s, u, v, a, t.
  2. Identify what the question is actually asking for.
  3. Cross out the one remaining quantity you don't have and don't need.
  4. Choose the equation missing that quantity.
Don't skip this step: jumping straight to a calculation is one of the most common ways marks are lost — you can easily reach for an equation that "looks right" but needs a value you were never given.

Sign convention

Choose one direction as positive at the start of a problem and stay consistent — it doesn't matter which direction you pick.

Ball thrown upwards (up = positive): u is positive; a is negative throughout (gravity always acts down — it does not flip sign at the top, only v does); v becomes negative once falling.

When can we use SUVAT?

Only valid while acceleration is constant. If it changes but is constant within separate stages, split the motion into multiple SUVAT problems — the final v of one stage becomes the initial u of the next.

  • Marble on a ramp: constant force → single-stage SUVAT.
  • Raindrop falling to terminal velocity: accelerates then levels off → acceleration isn't constant across the whole fall → SUVAT can't span it.
  • Lift: accelerates, constant velocity, decelerates → three separate stages, each solvable with SUVAT.

Displacement-time graphs

Displacement-time graph showing different stages of motion

Gradient = velocity; a curved section needs a tangent for instantaneous velocity.

Displacement is read directly from the y-axis. Gradient (Δs/Δt) = velocity: upward slope → positive velocity; steeper → greater magnitude. A curved line means changing velocity — draw a tangent to find the instantaneous velocity at a point.

Velocity-time graphs

Velocity-time graph showing different stages of motion

Gradient = acceleration; area under the line = displacement.

Gradient (Δv/Δt) = acceleration. Area under the line = displacement over that time. The line crosses the x-axis whenever the object momentarily stops; a horizontal line means constant velocity; a straight sloped line means constant acceleration.

Exam essentials

Key equations

  • v=u+at
  • s=(u+v)/2·t
  • s=ut+½at²
  • v²=u²+2as

Graph gradients & areas

  • s–t gradient = velocity.
  • v–t gradient = acceleration.
  • v–t area = displacement.

Common slips

  • Identify the missing quantity before calculating, not after.
  • g doesn't change sign at the top of a throw — only velocity does.
  • SUVAT needs constant acceleration — split multi-stage motion into separate applications.