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<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="UTF-8">
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<title>Uniformly Accelerated Motion</title>
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<body>
<header>
<h1>Uniformly Accelerated Motion</h1>
</header>
<h1>Uniformly Accelerated Motion (UAM)</h1>
<p><strong>Uniformly Accelerated Motion (UAM)</strong> refers to the motion of an object where its acceleration remains constant over time. This means the velocity of the object changes at a uniform rate.</p>
<h2>Key Variables in UAM</h2>
<ul>
<li><strong>Displacement (s)</strong>: The change in position of an object.</li>
<li><strong>Initial Velocity (u)</strong>: The velocity of the object at the start.</li>
<li><strong>Final Velocity (v)</strong>: The velocity of the object after time t.</li>
<li><strong>Acceleration (a)</strong>: The rate of change of velocity.</li>
<li><strong>Time (t)</strong>: The duration for which motion occurs.</li>
</ul>
<h2>Equations of Uniformly Accelerated Motion</h2>
<h3>1st Equation: Velocity-Time Relation</h3>
<div class="formula">v = u + at</div>
<h3>2nd Equation: Displacement-Time Relation</h3>
<div class="formula">s = ut + (1/2) a t²</div>
<h3>3rd Equation: Velocity-Displacement Relation</h3>
<div class="formula">v² = u² + 2as</div>
<h3>4th Equation: Average Velocity</h3>
<div class="formula">v_avg = (u + v) / 2</div>
<h2>Graphical Representation</h2>
<ul>
<li><strong>Velocity-Time Graph</strong>: A straight line with a slope equal to acceleration.</li>
<li><strong>Displacement-Time Graph</strong>: A parabolic curve for uniformly accelerated motion.</li>
</ul>
<h2>Special Cases in UAM</h2>
<h3>1. Free Fall Motion</h3>
<p>Acceleration due to gravity: g = 9.8 m/s² (downward)</p>
<div class="formula">v = u + gt</div>
<div class="formula">s = ut + (1/2) gt²</div>
<div class="formula">v² = u² + 2gs</div>
<h3>2. Motion on an Inclined Plane</h3>
<p>Acceleration along the plane: <strong>a = g sin(θ)</strong></p>
<h2>Derivations of Equations</h2>
<h3>1st Equation: v = u + at</h3>
<p>From acceleration definition:</p>
<div class="formula">a = (v - u) / t</div>
<p>Rearranging gives:</p>
<div class="formula">v = u + at</div>
<h3>2nd Equation: s = ut + (1/2) at²</h3>
<p>Velocity is the rate of change of displacement:</p>
<div class="formula">ds = v dt</div>
<p>Substituting v = u + at:</p>
<div class="formula">ds = (u + at) dt</div>
<p>Integrating:</p>
<div class="formula">s = ut + (1/2) at²</div>
<h3>3rd Equation: v² = u² + 2as</h3>
<p>Using v = u + at and solving for t, substituting into displacement formula:</p>
<div class="formula">v² = u² + 2as</div>
<h2>Applications of Uniformly Accelerated Motion</h2>
<ul>
<li><strong>Projectile Motion</strong> – Objects launched at an angle follow UAM in the vertical direction.</li>
<li><strong>Car Braking Systems</strong> – Deceleration calculations use UAM equations.</li>
<li><strong>Roller Coasters</strong> – The motion of carts follows UAM principles.</li>
</ul>
<p>This webpage covers the <strong>concepts, formulas, derivations, and applications</strong> of UAM.</p>
<footer>
<p>© 2025 Yoseph Feyisa Wegi | All Rights Reserved.</p>
</footer>
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