M9.3MechanicsCore

Constant Acceleration Formulae 1

The SUVAT equations link the five quantities of constant-acceleration motion: displacement s, initial velocity u, final velocity v, acceleration a, and time t. Pick the equation that uses the three you know plus the one you want.

30 min Constant Acceleration

Edexcel AS Level Maths: 9.3 Constant Acceleration Formulae 1Curated by Kepler, not produced by us. Watch it before the notes below.

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What you'll be able to do

Know the SUVAT variables
Use v = u + at
Use s = ½(u + v)t
Select the right equation for a problem

The SUVAT variables

The five quantities are $s$ (displacement), $u$ (initial velocity), $v$ (final velocity), $a$ (acceleration) and $t$ (time). Each SUVAT equation involves four of them, so you can solve any problem where three are known.

Two key equations

The first equation comes straight from “acceleration = change in velocity over time”. The second uses the average velocity over the time.

v = u + at

s

— links velocity, acceleration and time.

s = \tfrac{1}{2}(u + v)t

a

— uses the average velocity.

Example 1A car starts at 5 m/s and accelerates at 2 m/s² for 4 s. Find its final velocity.

1Use

v = u + at

5 + 2 \times 4

Answer

v = 13

m/s

Choosing an equation

List the SUVAT values you know and the one you want. Pick the equation containing exactly those four. A clear list at the start prevents using the wrong formula.

Tip — Write out s, u, v, a, t with the known values first — the right equation then jumps out.

Formula recap

v = u + at

Velocity–time (no s).

s = \tfrac{1}{2}(u + v)t

Displacement from average velocity (no a).

s, u, v, a, t

The five SUVAT quantities.

Common mistakes to avoid

Using SUVAT when the acceleration is not constant.

SUVAT only applies to constant (uniform) acceleration.

Mixing up u and v.

u is the initial velocity, v the final — list them clearly.

Key takeaways

SUVAT: s, u, v, a, t — for constant acceleration only.
v = u + at (no s); s = ½(u + v)t (no a).
List knowns and the unknown, then pick the matching equation.

Test yourself

Answer a few questions, then review anything you missed.

Next step

Keep practising

Start with the quiz above to check the key ideas. You can also choose another topic from the practice library.

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Related lessons

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Put the methods into practice: see how A-Level maths duels work. An account is required to play; the overview and sample are public.