Module 1 · Lesson

Equations of Motion

Kinematics

Equations of Motion

Orientation

Lesson goal: build accurate physics fluency for equations of motion and use that fluency to support clear HSC-style scientific writing.

This page is materialised into the MentorMind course shell from existing teaching, textbook, and eduKG material. Use it as the main lesson surface; use the tutor for targeted repair, worked examples, and concise writing feedback.

Source Lesson Material

Syllabus inquiry question

From The Feynman Lectures on Physics, Vol I, Chapter 8:

Galileo showed that constant acceleration turns motion into a mathematical problem. The equations of motion encode that idea in a form that is easy to apply.

Learning Objectives

Content

Assumptions for SUVAT

The equations apply to straight-line motion with constant acceleration. Air resistance and changing forces are neglected unless stated.

SUVAT equations only work when acceleration is constant. If acceleration varies, you must use calculus or graphical methods.

Core equations

The four SUVAT equations are:

$$v = u + at$$

$$s = ut + \frac{1}{2}at^2$$

$$v^2 = u^2 + 2as$$

$$s = \frac{(u+v)}{2}t$$

Where:

Equation Selection Guide

Missing VariableUse Equation
$s$$v = u + at$
$v$$s = ut + \frac{1}{2}at^2$
$u$$s = vt - \frac{1}{2}at^2$
$a$$s = \frac{(u+v)}{2}t$
$t$$v^2 = u^2 + 2as$

Problem-solving strategy

  1. List known variables with units.
  2. Identify the unknown variable.
  3. Choose an equation that includes the knowns and the unknown.
  4. Substitute, solve, and check sign conventions.

Interactive: SUVAT Equation Solver

Use this interactive tool to solve kinematics problems. Enter any three known values, and the solver will calculate the remaining two.

  1. Enter at least 3 known values (leave unknown fields empty)
  2. Click "Solve" to calculate the missing values
  3. The tool shows which equation was used

Worked Examples

Example 1: Final velocity

A cyclist starts at 3.0 m/s and accelerates at 0.80 m/s$^2$ for 5.0 s.

Known: $u = 3.0$ m/s, $a = 0.80$ m/s^2, $t = 5.0$ s Unknown: $v$

  1. Use $v = u + at$
  2. $v = 3.0 + (0.80)(5.0) = 3.0 + 4.0$
  3. $v = 7.0$ m/s

Velocity increases in the positive direction.

Example 2: Displacement under acceleration

A car travels at 10 m/s and accelerates at 1.5 m/s$^2$ for 4.0 s.

Known: $u = 10$ m/s, $a = 1.5$ m/s^2, $t = 4.0$ s Unknown: $s$

  1. Use $s = ut + \frac{1}{2}at^2$
  2. $s = (10)(4.0) + \frac{1}{2}(1.5)(4.0)^2$
  3. $s = 40 + 12 = 52$ m

Example 3: Stopping distance

A train slows uniformly from 22 m/s to rest over 110 m. Find the acceleration.

Known: $u = 22$ m/s, $v = 0$ m/s, $s = 110$ m Unknown: $a$

  1. Use $v^2 = u^2 + 2as$ (no $t$ needed)
  2. $0^2 = 22^2 + 2a(110)$
  3. $0 = 484 + 220a$
  4. $a = -2.2$ m/s^2

The negative sign indicates deceleration.

Example 4: Free fall

A ball is dropped from rest. How far does it fall in 3.0 s? (Take $g = 9.8$ m/s^2 downward)

Known: $u = 0$ m/s, $a = 9.8$ m/s^2, $t = 3.0$ s Unknown: $s$

  1. Use $s = ut + \frac{1}{2}at^2$
  2. $s = 0 + \frac{1}{2}(9.8)(3.0)^2$
  3. $s = 44$ m

Visualization: Motion Under Constant Acceleration

The graphs below show the relationship between position, velocity, and time for an accelerating object:

Observe:

Common Misconceptions

Practice Questions

Easy (2 marks)

A runner accelerates from rest at 2.0 m/s$^2$ for 3.0 s. Find final velocity.

Answer: $v = u + at = 0 + (2.0)(3.0) = 6.0$ m/s

Medium (4 marks)

A ball is thrown upward at 12 m/s. Ignore air resistance. Find the maximum height.

Answer:

Hard (5 marks)

A cart travels 25 m in 5.0 s with constant acceleration and finishes at 12 m/s. Find the initial velocity and acceleration.

Solution:

From $s = \frac{(u+v)}{2}t$:

From $v = u + at$:

Answers: $u = -2.0$ m/s, $a = 2.8$ m/s^2

Multiple Choice Questions

Test your understanding with these interactive questions:

Quick Quiz: SUVAT Problem Solving

Test your kinematics skills with this timed quiz:

Extended Response Practice

Summary

Self-Assessment

Check your understanding:

After studying this section, you should be able to:

Scientific Writing And Exam Support

When answering questions from this lesson, separate:

For explanation questions, write in the pattern: claim -> physics reason -> consequence. For calculation questions, state the formula, substitute with units, calculate, then interpret the answer.

Tutor Context

Use this lesson context when the student asks about equations of motion, related calculations, representations, or scientific writing. Prefer a short diagnostic before re-teaching. Check whether the student is confusing closely related categories such as force, velocity, acceleration, field, energy, momentum, model evidence, or mathematical representation.

Useful tutor diagnostic:

Which quantity is changing here, what causes that change, and what unit should the final answer use?

Maintenance Loop

One-minute retrieval:

  1. State the key law, model, or relationship used in this lesson.
  2. Identify one common misconception that would lead to a wrong answer.
  3. Write one sentence that links the calculation or evidence back to the physical meaning.

Source Trace

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