The total distance a steel ball rolls down an incline at...

The total distance a steel ball rolls down an incline at various times is given in Table $3-5$ a. Draw a position-time graph of the motion of the ball. When setting up the axes, use five divisions for each $10 \mathrm{m}$ of travel on the $d$ -axis. Use five divisions for 1 s of time on the $t$ -axis. b. Calculate the distance the ball has rolled at the end of $2.2 \mathrm{s}$ CANT COPY THE DATA

Key Concepts

Position-Time Graphs

A position-time graph is a visual representation of how an object's position changes over time. It helps in understanding and analyzing the motion by plotting time on the horizontal axis and position on the vertical axis. The slope of the graph gives information about the object's velocity, and any curvature in the graph can indicate acceleration or deceleration.

Graph Scaling

Graph scaling involves choosing appropriate divisions and labels for both axes to accurately represent the range of data. In this context, the position-time graph is scaled with specified divisions for distance and time, ensuring that changes in the object’s position over intervals of time are clearly and proportionally displayed, which is critical for both drawing and interpreting the motion.

Interpolation of Data

Interpolation is the process of estimating unknown values that fall between known data points. When data is provided at discrete time intervals, interpolation allows us to calculate approximate values, such as the distance traveled at a time that does not exactly match the measured points, by using the trend observed in the graph.

Uniformly Accelerated Motion

Uniformly accelerated motion refers to movement with a constant acceleration. For a rolling ball on an incline, assuming friction and other forces are negligible, the motion can be described by basic kinematic equations. This concept is important for understanding how the position changes non-linearly with time and for calculating distances and velocities at various time instants.

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