A woodpecker's brain is specially protected from large...

A woodpecker's brain is specially protected from large decelerations by tendon-like attachments inside the skull. While pecking on a tree, the woodpecker's head comes to a stop from an initial velocity of $0.600 \mathrm{m} / \mathrm{s}$ in a distance of only $2.00 \mathrm{mm} .$ (a) Find the acceleration in $\mathrm{m} / \mathrm{s}^{2}$ and in multiples of $g\left(g=9.80 \mathrm{m} / \mathrm{s}^{2}\right) .$ (b) Calculate the stopping time. (c) The tendons cradling the brain stretch, making its stopping distance $4.50 \mathrm{mm}$ (greater than the head and, hence, less deceleration of the brain). What is the brain's deceleration, expressed in multiples of $g$ ?

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Key Concepts

Acceleration Unit Conversion

Converting acceleration values to multiples of g (9.80 m/s²) offers a relatable measure of intensity, especially in contexts involving sudden accelerations or decelerations. This understanding helps compare calculated accelerations to the familiar gravitational acceleration experienced on Earth.

Stopping Time Calculation

The concept of stopping time involves determining the duration it takes for an object to come to rest from a given initial velocity under constant deceleration. By using the relationship t = ?v/a, one can calculate the time required to stop, which is fundamental in safety and impact analysis.

Uniform Acceleration Equations

Uniform acceleration equations, such as v² = v?² + 2a?x and v = v? + at, provide the mathematical framework needed to analyze motion with constant acceleration or deceleration. These formulas are essential for solving problems involving stopping distances and times.

Deceleration

Deceleration refers to negative acceleration—when an object's speed decreases over time. Understanding deceleration is crucial in scenarios where abrupt changes in motion occur, allowing the calculation of rates of slowing down and the forces involved.

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