In the Soapbox Derby, young participants build non-motorized...

In the Soapbox Derby, young participants build non-motorized cars with very lowfriction wheels. Cars race by rolling down a hill. The track at Akron's Derby Downs, where the national championship is held, begins with a 55 -ft-long section tilted $13^{\circ}$ below hori- $-$ -low hori-ted $13^{\circ}$ below hor zontal. a. What is the maximum possible acceleration of a car moving down this stretch of track? b. If a car starts from rest and undergoes this acceleration for the full $55 \mathrm{ft}$, what is its final speed in $\mathrm{m} / \mathrm{s}$ ?

In the Soapbox Derby, young participants build non-motorized cars with very lowfriction wheels. Cars race by rolling down a hill. The track at Akron's Derby Downs, where the national championship is held, begins with a 55 -ft-long section tilted $13^{\circ}$ below hori- $-$ -low hori-ted $13^{\circ}$ below hor
zontal.
a. What is the maximum possible acceleration of a car moving down this stretch of track?
b. If a car starts from rest and undergoes this acceleration for the full $55 \mathrm{ft}$, what is its final speed in $\mathrm{m} / \mathrm{s}$ ?

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Key Concepts

Inclined Plane Motion

This concept refers to analyzing how gravity affects an object that is moving on a slanted surface. The component of gravitational acceleration that propels the object down the incline is calculated using g multiplied by the sine of the angle of the slope. This is fundamental in determining the maximum acceleration experienced by an object on a frictionless inclined plane.

Kinematics of Constant Acceleration

Kinematics deals with the motion of objects under constant acceleration, using equations such as v² = u² + 2as, where v is the final velocity, u is the initial velocity, a is the acceleration, and s is the displacement. This principle is essential for calculating the final speed of an object that starts from rest and accelerates over a given distance on the incline.

Unit Conversion

Unit conversion is a crucial step in physics to ensure consistency and correct application of formulas, as different systems of units may be used. In problems like this, converting distances from feet to meters is necessary when the acceleration due to gravity is provided in meters per second squared, in order to correctly compute the final speed or other quantities.

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