Equations of motion

🎯 Learning Objectives

Learning Objectives (Cambridge AS A Level Curriculum)

2.1.1 Define and use distance, displacement, speed, velocity and acceleration
2.1.2 Use graphical methods to represent distance, displacement, speed, velocity and acceleration
2.1.6 Derive equations that represent uniformly accelerated motion in a straight line from the definitions of velocity and acceleration
2.1.3 Determine displacement from the area under a velocity–time graph
2.1.4 Determine velocity using the gradient of a displacement–time graph
2.1.5 Determine acceleration using the gradient of a velocity–time graph

🗣️ Language Objectives

Language Objectives

To describe physical quantities using correct terminology.
To interpret graphs of motion accurately.
To derive and apply kinematic equations using scientific language.
To explain motion using precise vocabulary in English.

📚 Vocabulary Table

Vocabulary Table

English Term	Russian Translation	Kazakh Translation
Distance	Расстояние	Арақашықтық
Displacement	Перемещение	Орын ауыстыру
Speed	Скорость	Жылдамдық
Velocity	Вектор скорости	Жылдамдық векторы
Acceleration	Ускорение	Үдеу

Flashcards on Quizlet

📘 Glossary

Glossary

Distance: The total length traveled by an object regardless of direction.
Displacement: The change in position of an object in a specific direction.
Speed: The rate at which an object covers distance without considering direction.
Velocity: The rate of change of displacement with respect to time, including direction.
Acceleration: The rate of change of velocity with respect to time.

📖 Theory

Equations of Motion (Cambridge AS A Level Physics)

In physics, when an object moves with -uniform acceleration-, we can use several equations to describe its motion:

v = u + at
s = ut + ½at²
v² = u² + 2as

Where:

v = final velocity
u = initial velocity
a = acceleration
t = time
s = displacement

🎥 Video Explanation

Watch this video for detailed explanation:

Worked Examples

Velocity-Time Graph — Example of velocity-time graph used to calculate acceleration.

Solution

Problem: A car starts from rest and reaches a speed of 20 m/s in 5 seconds. Calculate its acceleration.

Solution:
Given: Initial velocity u = 0 m/s, final velocity v = 20 m/s, time t = 5 s.
Using equation:

a = (v - u) / t

So,

a = (20 - 0) / 5 = 4 m/s²

🔍 Investigation Task

PhET Simulation

Answers

1. The car moved with constant acceleration when the velocity increased uniformly.
2. The maximum speed was reached after 10 seconds.
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👥 Group Activity

Group Task (LearningApps.org)

✍️ Individual Task

Structured Questions

A car accelerates from rest at 3 m/s² for 6 seconds. Find its final velocity.
Calculate the displacement if initial velocity is 4 m/s, final velocity is 16 m/s, and time is 5 seconds.
Find acceleration if displacement is 50 m, initial velocity is 0, and time is 5 seconds.
Draw a velocity-time graph for uniform acceleration and label it.
Derive the equation v = u + at.

Answer

1. v = u + at = 0 + 3×6 = 18 m/s
2. s = (u + v)/2 × t = (4 + 16)/2 × 5 = 50 m
3. s = ut + ½at² → 50 = 0 + ½a(25) → a = 4 m/s²
4. Draw a straight line graph increasing with time.
5. From definitions of velocity and acceleration.
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🔗 Useful Links

Useful Links

💭 Reflection

Reflection

What did you learn today?
Which part was the most difficult?
How will you apply these concepts in real life?