Question

you time an ant’s movement as it walks along a meter stick. you record the following data: {(0.0 s, 0.00 m), (1.0 s, 0.08 m), (2.0 s, 0.16 m)}. determine the ant’s velocity from the slope of the position vs. time graph.

Explanation:

Step1: Recall velocity - slope formula

The velocity \(v\) is given by the slope of the position - time graph, and the slope formula for two points \((t_1,x_1)\) and \((t_2,x_2)\) is \(v=\frac{x_2 - x_1}{t_2 - t_1}\).

Step2: Select two points

Let's take the first point \((t_1,x_1)=(0.0\ s,0.00\ m)\) and the second point \((t_2,x_2)=(1.0\ s,0.08\ m)\).

Step3: Calculate the velocity

Substitute the values into the slope formula: \(v=\frac{0.08\ m - 0.00\ m}{1.0\ s - 0.0\ s}\).
\[v=\frac{0.08\ m}{1.0\ s}=0.08\ m/s\]

Answer:

\(0.08\ m/s\)