Question

17 opción múltiple 1 punto
graph: position (m) on y-axis (ranging from -7 to 3), time (sec) on x-axis (ranging from 0 to 20). the graph shows a position-time plot with segments: starting at (0,0), then to (2,0), down to (5,-3), up to (7,0), up to (8,2), horizontal to (12,2), down to (14,-6), up to (16,-2), horizontal to (18,-2), up to (20,0).
when is the object moving in the negative direction, as shown by the graph?
○ 5-7 seconds, and 14-19 seconds
○ 2-6 seconds and 12.5-19 seconds
○ 0-2 seconds, 7-12 seconds, and 16-18 seconds
○ 2-5 seconds and 12-14 seconds

Explanation:

To determine when the object is moving in the negative direction, we analyze the position - time graph. An object moves in the negative direction when its position is decreasing as time increases (the graph has a negative slope).

Step 1: Analyze the slope of each interval

• For the interval \(2 - 5\) seconds: As time increases from \(2\) to \(5\) seconds, the position of the object decreases (the graph goes downwards), so the slope is negative, meaning the object is moving in the negative direction.
• For the interval \(12 - 14\) seconds: As time increases from \(12\) to \(14\) seconds, the position of the object decreases (the graph goes downwards), so the slope is negative, meaning the object is moving in the negative direction.

Let's check the other options:

• Option 1: In \(5 - 7\) seconds, the position is increasing (positive slope), so the object is moving in the positive direction. So this option is incorrect.
• Option 2: In \(2 - 6\) seconds, from \(5 - 6\) seconds the position is increasing (positive slope), so the object is not moving in the negative direction for the entire \(2 - 6\) seconds. So this option is incorrect.
• Option 3: In \(0 - 2\) seconds, the position is constant (slope = 0), in \(7 - 12\) seconds the position is constant (slope = 0), and in \(16 - 18\) seconds the position is constant (slope = 0). So the object is not moving in the negative direction in these intervals. So this option is incorrect.

Answer:

2 - 5 seconds and 12 - 14 seconds