A rolling ball moves from \( x_{1} = 8.5 \, \text{cm} \) to \( x_{2} = -4.7 \, \text{cm} \) during the time from \( t_{1} = 3.8 \, \text{s} \) to \( t_{2} = 6.7 \, \text{s} \).
What is its average velocity over this time interval?
Problem Statement:
A rolling ball moves from \( x_1 = 8.5 \, \text{cm} \) to \( x_2 = -4.7 \, \text{cm} \) during the time from \( t_1 = 3.8 \, \text{s} \) to \( t_2 = 6.7 \, \text{s} \).
Solution:
Step 1: Calculate Displacement (\( \Delta x \))
\[ \Delta x = x_2 - x_1 = -4.7 \, \text{cm} - 8.5 \, \text{cm} = -13.2 \, \text{cm} \]
Step 2: Calculate Time Interval (\( \Delta t \))
\[ \Delta t = t_2 - t_1 = 6.7 \, \text{s} - 3.8 \, \text{s} = 2.9 \, \text{s} \]
Step 3: Compute Average Velocity (\( \overline{v} \))
\[ \overline{v} = \frac{\Delta x}{\Delta t} = \frac{-13.2 \, \text{cm}}{2.9 \, \text{s}} \approx -4.6 \, \text{cm/s} \]
Final Answer:
\[ \boxed{-4.6 \, \text{cm/s}} \]
Note: The negative sign indicates direction (toward the negative \( x \)-axis). Rounded to two significant figures.
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