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<title>Adventure 6 — Starting Fast, Then Coming to a Stop</title>
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<a href="index.html"><button class="secondary">🧭 Hub</button></a>
<a href="adventure_6_story.html"><button class="secondary">📖 Story</button></a>
<a href="adventure_6_activity_1_student.html"><button class="secondary">✅ Activity 1</button></a>
<a href="adventure_6_activity_2_student.html"><button class="secondary">✅ Activity 2</button></a>
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<h1>🚀 Adventure 6 — Starting Fast, Then Coming to a Stop</h1>
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<b>Variable acceleration turns area into distance, and turns area into velocity — the visual heart of the Fundamental Theorem of Calculus.</b>.
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<h2>🎯 What you will learn</h2>
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<h3>Distance traveled = area under v(t).</h3>
<h3>Change in velocity = area under a(t).</h3>
<h3>Smaller time steps (Δt) give better rectangle estimates — your sums converge.</h3>
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<h2>📖 1) Read / Listen: Story</h2>
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<li>📖 <strong><a href="adventure_6_story.html">“Galileo and the Secret of Motion”</a></strong>
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<p>
Follow Galileo’s journey as he discovers how objects speed up and slow down — and how to measure it. You’ll see how he connected the dots between distance, velocity, and acceleration, and how his insights laid the groundwork for calculus.
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<h2>🎥 2. Watch the Video</h2>
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<strong><a href="https://www.youtube.com/watch?v=rfG8ce4nNh0&list=PLZHQObOWTQDMsr9K-rj53DwVRMYO3t5Yr&index=8" target="_blank" rel="noopener">3Blue1Brown — Integration and the fundamental theorem of calculus | Chapter 8, Essence of calculus</a></a></strong>
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<p>
See how motion builds piece by piece—and then gets “undone” by rates of change. You’ll see something surprising: adding up tiny pieces (of area) and measuring change (derivative) are actually opposite operations — one of the deepest ideas in calculus!
</p>
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<h2>✏️ 3) Do the Adventure 6 Activities</h2>
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<li>✏️ <strong><a href="adventure_6_activity_1_student.html">Activity 1</a></strong></li>
<p>Add up the area under a changing velocity graph to uncover total distance — and see how everything fits together.</p>
<li>✏️ <strong><a href="adventure_6_activity_2_student.html">Activity 2</a></strong></li>
<p>Connect what you see: distance from velocity, velocity from acceleration—and watch how area and change fit together perfectly.</p>
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