Category: CALCULUS

Verbally: "The rock’s velocity 3 seconds after being dropped."
Numerically: Time (s) | Position (m) ---------------------- 2.9 | -4.9 × (2.9)² ≈ -41.21 3.0 | -4.9 × (3.0)² = -44.1 3.1 | -4.9 × (3.1)² ≈ -47.29 Average velocity near t = 3: (-47.29 - (-41.21)) / 0.1 ≈ -60.8 m/s
Graphically: <img src="position-time-graph.png" alt="Position-time graph with tangent line at t=3" width="300"> The slope of the tangent line at t = 3 gives the instantaneous velocity.
Algebraically: s(t) = -4.9t² s'(t) = -9.8t At t = 3: s'(3) = -29.4 m/s

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