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Home » Average speed: \( \frac4207 = 60 \) km/h. - Coaching Toolbox

Average speed: \( \frac4207 = 60 \) km/h. - Coaching Toolbox

📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 A science communicator explains radioactive decay using a sample with a half-life of 8 years. If the initial mass is 200 grams, how much remains after 24 years?

📌 Number of half-lives: $ 24 / 8 = 3 $.

📌 Remaining mass = $ 200 \times (1/2)^3 = 200 \times 1/8 = 25 $ grams.

📌 A seismologist analyzes wave velocities through layers of Earth, finding that P-wave speed increases linearly with depth. At 10 km depth, speed is 6 km/s; at 30 km, it’s 7.5 km/s. What is the speed at 22 km?

📌 The rate of increase is $ (7.5 - 6) / (30 - 10) = 1.5 / 20 = 0.075 $ km/s per km.

📌 From 10 km to 22 km is 12 km, so increase = $ 12 \times 0.075 = 0.9 $ km/s.

📌 Speed at 22 km = $ 6 + 0.9 = 6.9 $ km/s.

📌 A theoretical physicist models dark energy density as a constant force field with strength $ \rho = k/ r^2 $, where $ r $ is distance from a point source. If $ \rho = 64 $ units at $ r = 2 $, what is $ \rho $ at $ r = 4 $?

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