A train is moving up a steep grade at constant velocity (see...

A train is moving up a steep grade at constant velocity (see following figure) when its caboose breaks loose and starts rolling freely along the track. After $5.0 \mathrm{s}$, the caboose is $30 \mathrm{m}$ behind the train. What is the acceleration of the caboose?

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Key Concepts

Motion on an Incline

Motion on an inclined plane deals with the component of gravitational acceleration acting along the direction of the incline. When friction is negligible, this component, often expressed as g sin?, determines the acceleration of an object rolling or sliding down the slope.

Uniformly Accelerated Motion

This concept involves the set of kinematic equations that describe the motion of objects with a constant acceleration. In such scenarios, relationships between displacement, initial velocity, time, and acceleration are established with equations like s = ut + 1/2 at², which is instrumental in solving problems where one of these variables is unknown.

Relative Motion

Relative motion examines the movement of one object in the frame of reference of another. When one object moves with constant velocity and another undergoes acceleration, analyzing their motion relative to each other—by considering relative displacement and acceleration—can simplify the problem-solving process.

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