The equations of motion: lesson plan (AS 9702, 2.1)

At a glance

The shape of the lesson

Topic

The equations of motion for uniform acceleration (subtopic 2.1)

Syllabus reference

Cambridge International AS & A Level Physics 9702, 2.1 (Topic 2: Kinematics)

Level

AS (first year)

Duration

60 minutes (single period, can extend to two)

Prior knowledge

Velocity-time graphs: gradient and area (the previous kinematics lesson)

Central visual model

The velocity-time graph that all four equations come from

Simulation

Free Fall and the Equations of Motion, applying suvat to a falling object

Cooperative structure

Jigsaw (full facilitation guide in the activity materials)

21st century skills

Collaboration, Communication, Critical Thinking

Assessment

An exit ticket and the individual Jigsaw quiz, both covering all four equations

Learning objectives

By the end of the lesson, learners can

AS (all learners)

recall the four equations for uniformly accelerated motion
derive each equation from a velocity-time graph
state that the equations apply only when the acceleration is constant
select the appropriate equation by identifying which quantity is missing
apply the equations to straight-line motion, including deceleration and the sign convention

Key vocabulary

uniform acceleration, initial velocity u, final velocity v, displacement s, time t, suvat, gradient, area, sign convention, deceleration. Each term is introduced as it is first needed.

The core ideas

Four equations from one graph

All four equations come from a single velocity-time graph for constant acceleration. The gradient gives v = u + a t; the area, a trapezium, gives s = ½(u + v)t; substituting one into the other gives s = u t + ½ a t²; and eliminating t gives v² = u² + 2 a s. The symbols are u, v, a, s and t.

A velocity-time graph for constant acceleration: the gradient is the acceleration and the trapezium area is the displacement, with initial velocity u, final velocity v and time t marked.

Gradient gives a; the trapezium area gives s

The four equations of motion, each labelled with the quantity it leaves out: v = u + a t omits s; s = half (u+v)t omits a; s = ut + half a t squared omits v; v squared = u squared + 2as omits t.

Each equation leaves out one quantity

Choose by the missing quantity

The fastest way to pick the right equation is to list u, v, a, s and t, then find the one quantity you neither know nor want: the equation that omits it is the one to use.

A guide to choosing the equation by the missing quantity: without s use v = u + a t; without a use s = half (u+v)t; without v use s = ut + half a t squared; without t use v squared = u squared + 2as.

List u, v, a, s, t; the missing one picks the equation

Deriving the equations from the graph

Where each one comes from

Equation	Comes from	Omits
v = u + a t	gradient of the velocity-time graph, a = (v − u) / t	s
s = ½(u + v) t	area under the graph (a trapezium)	a
s = u t + ½ a t²	substituting v = u + a t into the area	v
v² = u² + 2 a s	eliminating t between the first and third	t

Lesson sequence

Sixty minutes, phase by phase

Time	Phase	What happens in the room	Resources
0 to 5 min	Starter	Recall the gradient and area of a velocity-time graph from the last lesson.	Slide 1, fig-vt-derivation
5 to 15 min	Teach	Introduce the symbols and show how the graph gives the first two equations.	Slides 2 to 4
15 to 40 min	Activity	Jigsaw: expert groups master one equation each, then return home to teach it, so every group covers all four.	Jigsaw expert cards and home-group quiz
40 to 50 min	Model	Model selecting an equation by the missing quantity on a worked problem.	Slides 5 to 7, fig-equation-select
50 to 60 min	Plenary	Individual quiz to close the Jigsaw loop; review the trickiest item.	Home-group quiz on the activity sheet

Worked examples for the board

Choosing, and handling signs

Example 1: choose by the missing quantity

A car accelerates uniformly from 8.0 m s⁻¹ to 20 m s⁻¹ over a distance of 60 m. Find the acceleration and the time taken.

Time is missing, so use v² = u² + 2 a s: 20² = 8.0² + 2 a (60), so 400 = 64 + 120 a, giving a = 2.8 m s⁻²

Then v = u + a t: 20 = 8.0 + 2.8 t, so t = 12 / 2.8 = 4.3 s

Example 2: deceleration and signs

A car travelling at 30 m s⁻¹ brakes at 6.0 m s⁻². Find the stopping distance and the time to stop.

Sign convention: take the direction of motion as positive, so a = −6.0 m s⁻² and v = 0

Distance: v² = u² + 2 a s gives 0 = 30² + 2(−6.0)s, so s = 900 / 12 = 75 m

Time: v = u + a t gives 0 = 30 + (−6.0)t, so t = 5.0 s

A braking car starting at 30 metres per second decelerating at 6 metres per second squared, stopping after 75 metres in 5 seconds; with the motion direction positive the acceleration is negative.

Deceleration is an acceleration opposite to the motion

Running the cooperative task

Jigsaw

Home groups of four split the four equations between them, one each. Experts on the same equation meet to master its derivation, its use and a worked example, and rehearse how to teach it; they then return home and teach their equation in turn, so every home group ends up with all four. An individual quiz closes the loop. A full step-by-step facilitation guide, with the four expert cards and the home-group quiz and answer key, is provided as the activity in this bundle, so it can be run faithfully.

Master one equation, then teach your home group

Why it suits this lesson. The four equations are a natural set of four specialisms. A home group can only master all four if every expert delivers their part, and the individual quiz makes each learner accountable for the whole set, not just their own equation.

Examiner traps to pre-empt

What to head off, and how

Trap learners fall into	Teaching move that pre-empts it
Using the equations when the acceleration is not constant.	They hold only for uniform acceleration. If the v-t line is not straight, the equations do not apply.
Mixing sign conventions.	Choose one positive direction and keep it for u, v, a and s throughout the whole problem.
Treating deceleration as a separate rule.	Deceleration is simply an acceleration opposite to the velocity, so it carries a negative sign.
Reaching for s = u t + ½ a t² every time.	List the knowns first; pick the equation that does not contain the quantity you neither know nor want.

Differentiation and assessment

Support, challenge and the checks

Support: a list-the-knowns frame (u, v, a, s, t) so learners spot the missing quantity before choosing an equation.
Challenge: solve a two-stage journey (acceleration then constant velocity) and a problem where the object reverses direction.
Language: rehearse the frames "the quantity I do not need is ..." and "so I use ..." before learners commit to an equation.

Assessment is formative. Exit ticket question 1: a train starts from rest and accelerates at 0.50 m s⁻² for 20 s, find its final velocity and the distance travelled. Exit ticket question 2: state which equation you would use to find v when u, a and s are known, and explain why. The individual Jigsaw quiz covers all four equations.

Equipment and resources

the Jigsaw expert cards and home-group quiz, and the worksheet from this bundle
a list-the-knowns frame for support, and the exit ticket from the final slide
the site simulation Free Fall and the Equations of Motion, and the student topic page Equations of motion

Original work by the TheLucidSTEM team. Items are written in the style of the papers; no past paper question is reproduced. Supplied in editable formats so you can adapt them freely.

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