The system shown starts from rest, and each component moves...

The system shown starts from rest, and each component moves with a constant acceleration. If the relative acceleration of block $C$ with respect to collar $B$ is $60 \mathrm{mm} / \mathrm{s}^{2}$ upward and the relative acceleration of block $D$ with respect to block $A$ is $110 \mathrm{mm} / \mathrm{s}^{2}$ downward, determine $(a)$ the velocity of block $C$ after $3 \mathrm{s},(b)$ the change in position of block $D$ after $5 \mathrm{s}$.

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Key Concepts

Relative Motion and Frames of Reference

In mechanics, relative motion concerns how the position, velocity, and acceleration of one object appear from the perspective of a different moving object. This concept is crucial when one body’s motion is described with respect to another body that is itself in motion. In problems involving relative acceleration, the acceleration of one object relative to another is obtained by subtracting the acceleration of the reference object from the acceleration of the moving object, allowing one to analyze their kinematics in a non-inertial or moving reference frame.

Constant Acceleration Kinematics

Constant acceleration kinematics involves using equations that relate displacement, velocity, acceleration, and time for an object moving with a constant acceleration. Common equations include v = u + at and s = ut + 1/2at², where u is the initial velocity, v is the velocity at time t, a is acceleration, and s is displacement. This set of equations is essential for solving problems where the system's kinematic properties are analyzed over time, as they allow for the determination of final velocity and displacement from given acceleration and time.

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