Question

1. a man starts at the origin, walks towards the tree slowly and steadily for 6 seconds, then stands still for 6 seconds, and then turns around and walks towards the house steadily about twice as fast for 6 seconds. which of the following position versus time graphs also conveys this motion?

Explanation:

Step1: Analyze the first part of motion (walking towards the tree)

When the man walks slowly and steadily towards the tree, the position - time graph should have a positive - sloped straight line (since position is increasing with time) for the first 6 seconds.

Step2: Analyze the second part of motion (standing still)

When the man stands still, the position does not change with time. So, the graph should be a horizontal line (slope = 0) for the next 6 seconds (from \(t = 6\) s to \(t=12\) s).

Step3: Analyze the third part of motion (walking towards the house)

When the man walks towards the house steadily about twice as fast, the slope of the position - time graph (since \(v=\frac{\Delta x}{\Delta t}\), and slope of \(x - t\) graph gives velocity) should be steeper (negative slope because he is moving back towards the origin (assuming the tree is in the positive direction and house is in the negative direction relative to the origin)). Also, the time interval is 6 seconds.

Now let's check each option:

• Option A: The first part has a positive slope, then a horizontal line, and then a negative slope. But the time intervals are not 6 - 6 - 6.
• Option B: The first part has a negative slope (wrong direction as he starts from origin and walks towards the tree, which should be positive direction), then a horizontal line, and then a positive slope (wrong direction when coming back).
• Option C: The first part has a positive slope, then a horizontal line, and then a positive slope (wrong direction when coming back).
• Option D: The first part has a negative slope (wrong direction as he starts from origin and walks towards the tree, which should be positive direction).
• Option E: The first part is a horizontal line (wrong as he is moving in the first 6 seconds).
• Option F: The first part is a horizontal line (wrong as he is moving in the first 6 seconds).
• Option G: The first part is a horizontal line (wrong as he is moving in the first 6 seconds).
• Option H: The first part is a horizontal line (wrong as he is moving in the first 6 seconds).

Answer:

None of the options A - H are correct. But if we assume that the direction of the tree is considered as negative (opposite to the general assumption) and re - evaluate:
If we assume the tree is in the negative direction:

• Option B: First part (negative slope, moving towards the tree (negative direction)), then horizontal line (standing still), then positive slope (moving back towards the house (origin) twice as fast (steeper slope).

So, if we assume the direction of the tree is negative, the answer is B.