Theme A — Space, Time and Motion

A.1.4 Kinematic Equations — IB Physics HL Revision Notes & Topical Questions

5 min read 10 parts Lesson 6 of 63 1 quiz

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Lesson summary

A.1.4 Kinematic Equations — IB PHYSICS SL notes: Select and apply the equations of uniformly accelerated motion (suvat) to solve problems in one dimension.Kinematic equations — four equations describe any motion with constant (uniform) acceleration in a straight line.s — displace…

Choosing an equation
Data booklet
v = u + at
What the symbols mean
s = ½(u + v)t
s = ut + ½at2

Part 1 of 8The five variables

Kinematic equations

Kinematic equations four equations describe any motion with constant (uniform) acceleration in a straight line.

s displacement in m.

u initial velocity in m s⁻¹.

v final velocity in m s⁻¹.

a acceleration in m s⁻².

t time interval in s.

Part 2 of 8The four equations

Equation	Variable it leaves out
v = u + at	s
s = ut + ½at²	v
v² = u² + 2as	t
s = ½(u + v)t	a

Choosing an equation

Choosing an equation pick the one that contains the three known values and the one wanted, and leaves out the fifth variable.

Data booklet

Data booklet these equations are given in the data booklet and need not be memorised.

Part 3 of 8Where the equations come from

v u + at

it is the definition of acceleration rearranged.
What the symbols mean: v = final velocity (m s⁻¹) · u = initial velocity (m s⁻¹) · a = acceleration (m s⁻²) · t = time (s)

½(u + v)t

on a straight v–t graph the displacement is the area of a trapezium of average height ½(u + v) and width t.
What the symbols mean: s = displacement (m) · u = initial velocity · v = final velocity (m s⁻¹) · t = time (s); (u + v)/2 is the average velocity

s ut + ½at2

substitute v = u + at into s = ½(u + v)t.
What the symbols mean: s = displacement (m) · u = initial velocity (m s⁻¹) · a = acceleration (m s⁻²) · t = time (s)

v2 u2 + 2as

eliminate t between the first and fourth equations.
What the symbols mean: v = final velocity · u = initial velocity (m s⁻¹) · a = acceleration (m s⁻²) · s = displacement (m)

Validity

Validity the equations hold only when acceleration is constant.
They fail when the engine force changes or air resistance grows.

Part 4 of 8Hidden information in the wording

1Starts from rest

Starts from rest u = 0.

2Comes to rest

Comes to rest v = 0.

3Dropped

Dropped u = 0 and a = g.
- (positive downwards if down is positive)

4Falling due to gravity

Falling due to gravity a = 9.81 m s⁻² in the chosen sign convention.

5Constant speed

Constant speed a = 0.

6Constant acceleration in a straight line

Constant acceleration in a straight line a signal that the kinematic equations apply.

Part 5 of 8Method for solving problems

Choose a positive direction and use it for every vector (s, u, v and a).

Write down the known and unknown quantities, using the context to find hidden values.

Select the equation that contains the listed quantities and omits the fifth.

Convert units to SI, substitute, and rearrange to solve.

Check that the answer is reasonable and that its sign matches the direction.

Part 6 of 8Free fall and vertical motion

Free fall and vertical motion

Acceleration of free fall

Acceleration of free fall near Earth's surface, with air resistance ignored, every object accelerates at g = 9.8 m s⁻² downwards.
The equations use a = +g or a = −g depending on the sign convention.

Object thrown upwards

Object thrown upwards with up positive, a = −9.8 m s⁻² and the velocity is zero at the top.
The time up equals the time down when it returns to the same height.

Quadratic in t

Quadratic in t s = ut + ½at² often has two roots.
Reject a negative time, or note that the roots may be the upward and downward passes.

Part 7 of 8Stopping distance and multi-stage motion

1Braking distance

Braking distance with v = 0, s = u² / (2|a|).
Doubling the initial speed quadruples the braking distance for the same deceleration.

2Two-stage motion

Two-stage motion the final velocity of one stage is the initial velocity of the next.
Treat each stage with its own suvat values, then add the displacements or times.

3Two objects meeting

Two objects meeting write each displacement in terms of the same time t and equate them.
This gives a single equation, often a quadratic.

Part 8 of 8More from the specification

Key terms

Term	Meaning
Uniform acceleration	Constant acceleration, required for the suvat equations
suvat	Shorthand for displacement s, initial velocity u, final velocity v, acceleration a and time t
Free fall	Motion under gravity only
Braking distance	Distance travelled while decelerating to rest
Initial velocity	Velocity at t = 0
Sign convention	Choice of positive direction applied to all vectors

Avoid these mistakes

Using the equations when acceleration is not constant — they apply only to uniform acceleration.

Mixing sign conventions, for example using +g with up positive — keep one convention throughout.

Forgetting hidden values — at rest means u = 0 or v = 0.

Dropping the square on t or on the velocities — v² = u² + 2as and s = ut + ½at².

Choosing an equation with an unwanted unknown — choose the one that omits the unneeded variable.

Last updated: 15 October 2026