Rectilinear Acceleration, Units, Uniform Motion for SS 1

Class: SS 1
Term: First Term
Week: 7
Age: 15 years
Duration: 60 minutes
Subject: Physics
Curriculum Theme: Interaction of matter, space, and time
Focal competence: Plotting graphs and determining acceleration from velocity-time graphs
Key competencies/values: Creativity and Innovation; Collaboration; Research and Problem Solving; Problem Solving; Resilience
Skills:

• Plotting of velocity-time graphs and deducing acceleration from the graph

Previous Lesson: Scalar and Vector Quantities, Differences
Topic: Rectilinear Acceleration
Subject Matter: Meaning of Rectilinear acceleration, Meaning of acceleration and its unit, Meaning of uniform motion, Calculation of the area under the velocity-time graph

Specific Objectives

By the end of the lesson, pupils/students should be able to:

Cognitive Domain

• Define acceleration.
• State the unit of acceleration.
• Explain the concept of uniform motion.
• Derive the formula of acceleration.

Psychomotor Domain

• Plot velocity-time graphs.
• Deduce acceleration from a velocity-time graph.

Reference Materials

The following resources were used in planning this lesson:

• 2025 New Revised Senior Secondary Education Curriculum (SSEC)
• Relevant State Unified Scheme of Work
• New School Physics for Senior Secondary Schools by M.W. Anyakoha
• The HeadTeacher Scheme of work For The New Revised Senior Secondary Education Curriculum (SSEC)

Instructional Materials

The teacher will teach this lesson with the aid of:

• Ticker timer and accessories
• Graph sheets
• Ruler
• Pencil
• Pair of scissors
• Whiteboard/Blackboard
• Markers/Chalk

Rationale for the Lesson

This lesson provides students with a foundational understanding of how motion changes over time, which is essential for describing and predicting the movement of objects. It helps them develop analytical skills through graph interpretation and problem-solving, connecting abstract physics concepts to real-world phenomena.

Prerequisite/Previous Knowledge

Students should have prior knowledge of speed, velocity, displacement, distance, and time, including their definitions and units.

Lesson Content/Board Summary

Rectilinear Acceleration

Meaning of Rectilinear Acceleration

Rectilinear acceleration refers to the rate of change of velocity of an object moving along a straight line. It describes how quickly the velocity of an object changes in a specific direction without any change in the direction of motion.

Meaning of Acceleration and its Unit

Acceleration is defined as the rate of change of velocity. It is a vector quantity, meaning it has both magnitude and direction. An object accelerates if its speed changes, or its direction of motion changes, or both.

Formula for Acceleration:

(a = frac{text{Change in velocity}}{text{Time taken}} = frac{v – u}{t})

Where:

1. (a) = acceleration
2. (v) = final velocity
3. (u) = initial velocity
4. (t) = time taken

Unit of Acceleration:

The SI unit of velocity is metres per second ((m/s)), and the SI unit of time is seconds ((s)). Therefore, the SI unit of acceleration is metres per second squared ((m/s^2)).

Acceleration is a derived quantity, meaning it is formed from fundamental quantities like length (metres) and time (seconds). It is important to distinguish between a physical quantity (like acceleration) and its unit (like (m/s^2)) and to use consistent units in all calculations.

Meaning of Uniform Motion

Uniform motion (or uniform velocity) occurs when an object moves with a constant velocity. This means that the object covers equal distances in equal intervals of time along a straight line. In uniform motion, the speed and direction of the object remain unchanged.

Characteristics of Uniform Motion:

1. The velocity of the object is constant.
2. The acceleration of the object is zero.
3. The object moves in a straight line.

Velocity-Time Graphs

A velocity-time graph plots the velocity of an object on the vertical (y) axis against time on the horizontal (x) axis. These graphs are useful for analysing motion and determining acceleration and displacement.

Deducing Acceleration from a Velocity-Time Graph:

The gradient (slope) of a velocity-time graph represents the acceleration of the object. A steeper slope indicates a greater acceleration, while a horizontal line indicates zero acceleration (uniform velocity).

(text{Acceleration (a)} = frac{text{Change in velocity}}{text{Change in time}} = frac{Delta v}{Delta t} = frac{v_2 – v_1}{t_2 – t_1})

Calculating Displacement from the Area Under a Velocity-Time Graph:

The area under a velocity-time graph represents the displacement of the object. The shape formed by the graph line and the time axis can be a rectangle, triangle, or trapezium, and its area can be calculated using standard geometric formulas.

1. For a rectangle (uniform velocity): Area = length × breadth = velocity × time
2. For a triangle (uniform acceleration from rest): Area = ( frac{1}{2} times text{base} times text{height} = frac{1}{2} times text{time} times text{final velocity} )
3. For a trapezium (uniform acceleration with initial velocity): Area = ( frac{1}{2} times (text{sum of parallel sides}) times text{height} = frac{1}{2} times (u + v) times t )

Example 1

Question: A car starts from rest and accelerates uniformly to a velocity of 20 m/s in 5 seconds. It then maintains this velocity for another 10 seconds. Calculate:

1. The acceleration of the car during the first 5 seconds.
2. The total displacement of the car.

Solution:

Part 1: Acceleration during the first 5 seconds

Step 1: Identify initial and final velocities and time.

(u = 0 , m/s) (starts from rest)
(v = 20 , m/s)
(t = 5 , s)

Step 2: Write the formula for acceleration.

(a = frac{v – u}{t})

Step 3: Substitute the values and calculate.

(a = frac{20 , m/s – 0 , m/s}{5 , s} = frac{20 , m/s}{5 , s} = 4 , m/s^2)

Answer: The acceleration during the first 5 seconds is (4 , m/s^2).

Part 2: Total Displacement

To calculate total displacement, we can consider the area under the velocity-time graph. The motion consists of two parts: uniform acceleration (first 5 seconds) and uniform velocity (next 10 seconds).

Step 1: Calculate displacement during uniform acceleration (first 5 seconds).

This forms a triangle on the velocity-time graph (from (0,0) to (5,20)).

(text{Displacement}_1 = frac{1}{2} times text{base} times text{height} = frac{1}{2} times 5 , s times 20 , m/s = 50 , m)

Step 2: Calculate displacement during uniform velocity (next 10 seconds).

This forms a rectangle on the velocity-time graph (from (5,20) to (15,20)).

(text{Displacement}_2 = text{velocity} times text{time} = 20 , m/s times 10 , s = 200 , m)

Step 3: Calculate total displacement.

(text{Total Displacement} = text{Displacement}_1 + text{Displacement}_2 = 50 , m + 200 , m = 250 , m)

Answer: The total displacement of the car is (250 , m).

Teaching Methods/Instructional Techniques

Discussion, Demonstration, Guided Practice, Question and Answer, Explanation, Problem Solving, Group Work

Instructional Procedures

Step 1: Introduction

Time: 5 minutes

Teaching Skill: Recalling/Engaging

Teacher’s Activity: The teacher greets the students and asks them to recall what they learned about speed, velocity, and displacement in the previous lesson. The teacher then introduces the topic of rectilinear acceleration.

Pupils’ Activity: Pupils respond to questions about speed, velocity, and displacement.

Learning Point: Prior knowledge activation

Step 2: Meaning of Rectilinear Acceleration

Time: 5 minutes

Teaching Skill: Explanation

Teacher’s Activity: The teacher explains the meaning of rectilinear acceleration as the rate of change of velocity along a straight line, giving simple examples like a car speeding up or slowing down on a straight road.

Pupils’ Activity: Pupils listen attentively and ask questions for clarification.

Learning Point: Rectilinear acceleration meaning

Step 3: Acceleration and its Unit

Time: 8 minutes

Teaching Skill: Discussion/Explanation

Teacher’s Activity: The teacher guides students in a group discussion on the meaning of acceleration, its formula, and its SI unit. The teacher explains how acceleration is a derived quantity from fundamental units and stresses consistent unit use.

Pupils’ Activity: Students participate in group discussions, define acceleration, state its formula and unit, and discuss derived quantities.

Learning Point: Acceleration definition, unit

Step 4: Uniform Motion

Time: 5 minutes

Teaching Skill: Explanation

Teacher’s Activity: The teacher explains the concept of uniform motion, highlighting that it means constant velocity and zero acceleration. The teacher provides examples of objects in uniform motion.

Pupils’ Activity: Pupils listen and identify characteristics of uniform motion.

Learning Point: Uniform motion concept

Step 5: Introduction to Velocity-Time Graphs

Time: 7 minutes

Teaching Skill: Demonstration/Explanation

Teacher’s Activity: The teacher introduces velocity-time graphs, explaining how they are plotted and what the axes represent. The teacher shows examples of graphs for uniform velocity and uniform acceleration.

Pupils’ Activity: Pupils observe the graph examples and understand the plotting conventions.

Learning Point: Velocity-time graph plotting

Step 6: Deducing Acceleration and Displacement from Graphs

Time: 10 minutes

Teaching Skill: Guided Practice/Problem Solving

Teacher’s Activity: The teacher guides students to deduce acceleration from the gradient of a velocity-time graph and to calculate displacement from the area under the graph, using the provided example from the Board Summary. Students use graph sheets, rulers, and pencils to practice.

Pupils’ Activity: Pupils actively participate, plot simple graphs, calculate gradients for acceleration, and determine areas for displacement.

Learning Point: Graph interpretation skills

Step 7: Evaluation/Review

Time: 5 minutes

Teaching Skill: Questioning/Assessment

Teacher’s Activity: The teacher evaluates the learning by asking the following questions:

1. What is rectilinear acceleration?
2. Define acceleration and state its SI unit.
3. Explain what is meant by uniform motion.
4. How can you deduce acceleration from a velocity-time graph?

Pupils’ Activity: Pupils answer orally and in writing.

Learning Point: Understanding acceleration concepts

Step 8: Note-Taking

Time: 10 minutes

Teaching Skill: Guided Writing

Teacher’s Activity: The teacher guides pupils/students to copy the essential Board Summary notes, including definitions, formulas, and the worked example, into their notebooks.

Pupils’ Activity: Pupils/students copy the notes carefully into their notebooks.

Learning Point: Board summary recording

Step 9: Conclusion

Time: 5 minutes

Teaching Skill: Summarising

Teacher’s Activity: The teacher briefly summarises the main points of the lesson, reiterating the definitions of rectilinear acceleration, acceleration, uniform motion, and the importance of velocity-time graphs in analysing motion. The teacher encourages students to practice plotting and interpreting graphs.

Pupils’ Activity: Pupils listen and ask any final questions.

Learning Point: Lesson concept consolidation

Continuous Assessment/Further Study

Type: Homework/Practice Exercise

Instruction: Answer the following questions in your notebook:

1. A motorcycle accelerates from 10 m/s to 30 m/s in 4 seconds. Calculate its acceleration.
2. Describe two characteristics of an object undergoing uniform motion.
3. Draw a velocity-time graph for an object that starts from rest, accelerates uniformly to 15 m/s in 3 seconds, and then maintains that velocity for another 5 seconds.
4. From your graph in question 3, calculate the total displacement of the object.

Lesson Keywords

• Rectilinear – moving in a straight line
• Acceleration – rate of change of velocity
• Velocity – speed in a given direction
• Uniform Motion – motion at a constant velocity (zero acceleration)
• Gradient – slope of a line on a graph
• Displacement – overall change in position
• SI Unit – International System of Units

Differentiation

For students who grasp concepts quickly, provide more complex velocity-time graph scenarios involving deceleration or multiple phases of motion. For students needing additional support, provide pre-drawn graph templates and guide them step-by-step through the calculation of gradient and area, focusing on one concept at a time.

Suggested Lesson Videos

Search YouTube for “rectilinear acceleration velocity time graph SS1 physics”