The displacement versus time for a certain particle moving...

The displacement versus time for a certain particle moving along the $x$ axis is shown in Figure $\mathrm{P} 2.3 .$ Find the average velocity in the time intervals (a) 0 to $2 \mathrm{~s}$, (b) 0 to $4 \mathrm{~s}$, (c) $2 \mathrm{~s}$ to $4 \mathrm{~s}$, (d) $4 \mathrm{~s}$ to $7 \mathrm{~s}$, (e) 0 to $8 \mathrm{~s}$.

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Key Concepts

Displacement vs. Time Graph

A displacement vs. time graph displays how an object's position changes over a period of time. In this graph, the horizontal axis usually represents time, and the vertical axis represents displacement. The shape and slope of the graph give insight into the object's motion, including periods of constant velocity, acceleration, and potential changes in direction.

Average Velocity

Average velocity is defined as the total displacement divided by the total time taken during a specific interval. It is calculated by taking the difference between the final and initial displacements and dividing by the time difference. This concept captures the overall rate of change of position over an interval, regardless of the details of the motion in between.

Time Interval

A time interval refers to a specific period during which observations or measurements are made. In the context of motion, analyzing different time intervals can reveal how the velocity or behavior of an object changes over distinct segments of its journey, which is crucial for understanding variations in motion such as accelerations or decelerations.

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