Question

calculate the slope of the line segment from t = 1 s to t = 3 s. a 5 m/s b 10 m/s c 20 m/s d 25 m/s a position - time graph is shown. position vs. time

Explanation:

Step1: Identify two - point coordinates

At \(t = 1s\), the position \(x_1=20m\); at \(t = 3s\), the position \(x_2 = 0m\).

Step2: Use slope formula

The slope formula for a position - time graph is \(v=\frac{\Delta x}{\Delta t}=\frac{x_2 - x_1}{t_2 - t_1}\). Substitute \(x_1 = 20m\), \(x_2=0m\), \(t_1 = 1s\), \(t_2 = 3s\) into the formula: \(\frac{0 - 20}{3 - 1}=\frac{- 20}{2}=-10m/s\). The magnitude of the slope (speed) is \(10m/s\).

Answer:

\(10m/s\)