Class 11 > Unit # 02: Kinematics >Equations of Motion

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Unit # 2: Kinematics — Equations of Motion by Graphical Method

Lecture Overview

This video covers the step-by-step derivations of the equations of motion using the graphical method as part of Unit 2 (Kinematics) for Class 11 Physics under the Sindh Board / Board of Intermediate Education Karachi curriculum.

Source Video: Equations of motion by graphical method - Unit 2 Kinematics - Class 11 Physics

1. Detailed Explanation of the Speed-Time Graph

In this lecture, Sir Talha explains how to set up and interpret the speed-time (or velocity-time) graph for an object moving along a straight line with uniform acceleration:

• Axes Representation: Time (\(t\)) is plotted along the horizontal axis ($x$-axis), while velocity (\(v\)) is plotted along the vertical axis ($y$-axis).
• Initial Velocity (\(v_i\)): At time \(t = 0\), the object is not at rest; it starts with an initial velocity represented by point \(A\) on the vertical axis (segment \(OA\)).
• Final Velocity (\(v\)): Due to uniform acceleration \(a\), the velocity increases uniformly over time \(t\) up to point \(B\), so that the final velocity corresponds to point \(C\) on the vertical axis (\(OC = v\)).
• The Graph Line (\(AB\)): The straight sloped line \(AB$ represents constant acceleration. Dropping perpendicular lines from point \(B$ to the axes establishes the geometric boundaries used for subsequent mathematical derivations.

2. Derivations Covered in the Lecture

First Equation of Motion

Relates final velocity (\(v\)), initial velocity (\(v_i\)), acceleration (\(a\)), and time (\(t\)):

$$v = v_i + at$$

Derived by evaluating the slope of line \(AB\) on the velocity-time graph, where acceleration equals the rise divided by the run (\(\text{BC} / \text{AC}\)).

Second Equation of Motion

Relates total distance or displacement (\(S\)) with initial velocity, time, and acceleration:

$$S = v_i t + \frac{1}{2}at^2$$

Derived by calculating the total area enclosed under the graph line \(AB\), which is divided into a rectangle (\(\text{OADC}\)) and a right-angled triangle (\(\text{ABD}\)).

Third Equation of Motion

Relates velocity, acceleration, and displacement independently of time:

$$2aS = v^2 - v_i^2$$

Derived by treating the entire geometric shape under line \(AB$ as a trapezium (\(\text{OABC}\)) and applying its area formula: \(\text{Area} = \frac{\text{Sum of parallel sides}}{2} \times \text{height}\).

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