Constant Acceleration in 1D

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Edexcel IAL · Mechanics 1

Constant Acceleration in 1D

When an object moves in a straight line at constant acceleration, five linked equations — the suvat equations — let you find any unknown of the motion from just three known values.

3 Main Topics 5 Equations to Memorise Worked Examples Included Concepts Checklist

Chapter Overview

suvat variables — five quantities describing any straight-line constant-acceleration motion

5 equations — each connects 4 of the 5 variables; know 3, find the 4th

Derivation from v-t graph — gradient = acceleration; area = displacement

Vertical motion — same equations apply; gravity gives a = ±9.8 m s⁻²

Displacement ≠ distance — direction matters; know which one you're finding

Multi-stage problems — split into phases; the final v of one stage = initial u of the next

The suvat Variables

suvat is an acronym made from the five quantities that describe any straight-line motion with constant acceleration:

Letter	Quantity	Unit	Notes
s	Displacement	metres (m)	Vector — measured from the starting point. Can be negative.
u	Initial velocity	m s⁻¹	Vector — velocity at the start of the time period. Can be negative.
v	Final velocity	m s⁻¹	Vector — velocity at the end of the time period. Can be negative.
a	Acceleration	m s⁻²	Vector — must be constant throughout. Negative means deceleration.
t	Time	seconds (s)	Scalar — always positive (we can't go backward in time!).

Vector vs Scalar

Four of the five quantities (s, u, v, a) are vectors — they have a direction. A negative value simply means the opposite direction to the one you defined as positive. Time (t) is a scalar — it's always positive.

Think of it like a road trip: You start at a position (s tells you how far from home you've gone), you begin driving at a certain speed (u), you end at another speed (v), your engine gives you a constant push or braking force (a), all over a duration of time (t). Knowing any three of these, you can calculate the others.

The Five suvat Equations

There are exactly five equations. Each one links a different set of four variables. They are not given in the exam — you must memorise all five.

v = u + at

Missing: s

v² = u² + 2as

Missing: t

s = ½(u + v)t

Missing: a

s = ut + ½at²

Missing: v

s = vt − ½at²

Missing: u

The Golden Rule

Identify which 3 variables you know and which 1 you want. Then pick the equation that contains all four of those — and doesn't need the one you don't know (the "missing" variable).

How to Derive the Equations

The four equations involving t come directly from a velocity-time (v-t) graph. Because acceleration is constant, the graph is a straight line:

What to Memorise

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Constant Acceleration in 1D

Constant Acceleration in 1D

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