Question

14 opción múltiple 1 punto

according to the graph above, when is the object accelerating?

• from 1 to 3 seconds only
• from 1-3 and from 4.5-6 seconds
• from 0-1 and from 3-4.5 seconds
• none of these

Explanation:

To determine when the object is accelerating, we analyze the position - time graph. In a position - time graph, the slope of the graph represents the velocity of the object. Acceleration occurs when there is a change in velocity (either a change in speed or direction). A constant slope means constant velocity (zero acceleration), and a changing slope means a change in velocity (acceleration).

Step 1: Analyze the slope in different time intervals

• Interval 0 - 1 seconds: The slope of the graph is 0 (the graph is horizontal). This means the velocity \(v=\frac{\Delta x}{\Delta t} = 0\) (constant velocity, so acceleration \(a = 0\)).
• Interval 1 - 3 seconds: The slope of the graph is positive and constant (the graph is a straight line with a positive slope). So the velocity is constant (since the slope is constant), and acceleration \(a=0\).
• Interval 3 - 4.5 seconds: The slope of the graph is 0 (the graph is horizontal). So the velocity is constant (\(v = 0\)) and acceleration \(a = 0\).
• Interval 4.5 - 6 seconds: The slope of the graph is negative and constant (the graph is a straight line with a negative slope). So the velocity is constant (since the slope is constant), and acceleration \(a = 0\).

Since in all the intervals, the velocity is constant (the slope of the position - time graph is constant), there is no acceleration (change in velocity) in any of the intervals.

Answer:

D. None of these