Question

position vs time
calculate the slope of the line on the graph using the
formula:

the slope of the line is m/s.

Explanation:

Step1: Identify two points on the line

We can take the points \((x_1, y_1) = (0, 0)\) and \((x_2, y_2) = (5, 18)\) (from the graph, at \(x = 5\) s, \(y = 18\) m? Wait, wait, looking at the graph, when \(x = 5\), the position is 18? Wait no, the y-axis is position (m), and the grid: at \(x = 1\), \(y = 4\); \(x = 2\), \(y = 8\); \(x = 3\), \(y = 12\); \(x = 4\), \(y = 16\); \(x = 5\), \(y = 20\)? Wait, the top is 20. So let's take \((0, 0)\) and \((5, 20)\) or maybe \((1, 4)\) and \((5, 20)\). Let's use \((x_1, y_1) = (0, 0)\) and \((x_2, y_2) = (5, 20)\) (since at \(t = 0\) s, position is 0 m; at \(t = 5\) s, position is 20 m).

Step2: Apply the slope formula

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Substituting \(x_1 = 0\), \(y_1 = 0\), \(x_2 = 5\), \(y_2 = 20\) into the formula:
\(m=\frac{20 - 0}{5 - 0}=\frac{20}{5}=4\)

Wait, let's check with another pair. Take \((1, 4)\) and \((2, 8)\): \(m=\frac{8 - 4}{2 - 1}=\frac{4}{1}=4\). Yep, so the slope is 4.

Answer:

4