Question

9 opción múltiple 1 punto
graph: position x (m) vs time t (s), with segments a (from (0,0) to ~40s, 30m), b (flat from ~40s to ~80s), c (decreasing from ~80s to 160s)
based on the graph, when is the object moving fastest?
options: c, a, b, not possible to determine

Explanation:

In a position - time graph, the slope of the graph represents the velocity (speed, considering magnitude) of the object. A steeper slope means a higher speed.

• For segment A: Let's assume the time interval for A is from \(t = 0\) to \(t=40\) s (approximate from the graph) and the position changes from \(x = 0\) to \(x = 30\) m. The slope (speed) \(v_A=\frac{\Delta x}{\Delta t}=\frac{30 - 0}{40-0}=\frac{30}{40} = 0.75\) m/s.
• For segment B: The slope is 0 (since the position is constant), so the speed \(v_B = 0\) m/s.
• For segment C: Let's assume the time interval for C is from \(t = 80\) s to \(t = 160\) s and the position changes from \(x = 30\) m to \(x = 10\) m. The slope (speed, magnitude) \(v_C=\frac{\Delta x}{\Delta t}=\frac{30 - 10}{160 - 80}=\frac{20}{80}=0.25\) m/s.

Comparing the speeds, \(v_A>v_C > v_B\). So the object is moving fastest in segment A.

Answer:

B. A