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When discussing the concept of change in position, it refers to how far an object has moved from its initial point to its final one. It is an essential part of understanding motion. Change in position is denoted by \( \Delta x \), and it is calculated as the difference between two positions: the final position \( x_2 \) and the initial position \( x_1 \). 1. Formula: - \( \Delta x = x_2 - x_1 \) - - This formula tells us the net change in where the object is located.In the given exercise, the position of the ball changes from \( x_1 = 3.4 \, \text{cm} \) to \( x_2 = -4.2 \, \text{cm} \). Calculating this gives us \( \Delta x = -4.2 \, \text{cm} - 3.4 \, \text{cm} = -7.6 \, \text{cm} \).The negative sign indicates that the object moved in the opposite direction on the axis from the positive starting point. Understanding this directionality in motion is crucial, especially when interpreting real-world movements.

The change in time, often symbolized as \( \Delta t \), measures the duration over which the change in position occurs. This is a key element in many physics calculations, especially those involving motion.1. Understanding change in time:- It allows us to quantify how long an event lasts, providing a sense of speed and movement over periods.2. Formula: - \( \Delta t = t_2 - t_1 \)To calculate it, we subtract the start time \( t_1 \) from the end time \( t_2 \). In the exercise example, the time changes from \( t_1 = 3.0 \, \text{s} \) to \( t_2 = 5.1 \, \text{s} \), resulting in \( \Delta t = 5.1 \, \text{s} - 3.0 \, \text{s} = 2.1 \, \text{s} \).This calculated duration helps us to compare how fast different objects move, given the same or different durations. Time change helps identify not only the efficiency of a motion but also its nature across varying lengths of cycles.

Velocity calculation is central to understanding how fast something moves in a particular direction. Average velocity is a straightforward way to express this. We compute it by dividing the change in position by the change in time.1. Formula:- \( v_{avg} = \frac{\Delta x}{\Delta t} \) This ratio gives us a clear view of how rapid the movement was, with direction included due to the sign (positive or negative) of \( \Delta x \).2. Example Calculation:- Using the previous calculations: - The change in position \( \Delta x = -7.6 \, \text{cm} \) - The change in time \( \Delta t = 2.1 \, \text{s} \)Using these values in the velocity formula:\[ v_{avg} = \frac{-7.6 \, \text{cm}}{2.1 \, \text{s}} \approx -3.62 \, \text{cm/s} \] This result shows us that the object moved at an average speed of \(-3.62 \, \text{cm/s}\), and the negative value indicates its direction. The concept of velocity changes our understanding of motion by linking time, distance, and direction together, providing a comprehensive picture of an object's movement over time.