Question

1. the distance time graph shows carlos motion in front of a sensor.

a) identify the d - intercept and explain what it means
b) identify the t - intercept and explain what it means
c) describe the instructions you would give someone walking in front of a sensor to reproduce this graph

Explanation:

Part a)

Step1: Find d - intercept

The d - intercept is the value of \(d\) when \(t = 0\). From the graph, when \(t=0\), \(d = 0\) m.

Step2: Explain the d - intercept

The \(d\) - intercept represents the initial distance of Carlo from the sensor. At time \(t = 0\) (the start of the measurement), Carlo is \(0\) meters away from the sensor, meaning he starts at the sensor's location.

Step1: Find t - intercept

The \(t\) - intercept is the value of \(t\) when \(d=0\). From the graph, when \(d = 0\), \(t=7\) s.

Step2: Explain the t - intercept

The \(t\) - intercept represents the time when Carlo is back at the sensor (distance from sensor is \(0\) m). After \(7\) seconds of walking, Carlo returns to the position of the sensor.

1. Start at the sensor (distance \(0\) m from sensor) at time \(t = 0\).
2. Walk away from the sensor at a constant speed. The slope of the graph (change in distance over change in time) can be calculated. From \(t = 0\) to \(t=7\) s, distance changes from \(0\) m to \(3\) m? Wait, no, looking at the graph, when \(t = 7\) s, \(d = 0\), and at \(t = 0\), \(d = 0\), and there is a line from \((0,0)\) to \((7,0)\)? Wait, no, the graph has a line from \((0,0)\) to \((7,3)\)? Wait, the grid: Let's re - examine. The \(d\) - axis (distance) has marks \(0,1,2,3,4,5\) and \(t\) - axis (time) has marks \(0,1,2,3,4,5,6,7\). The line goes from \((0,0)\) to \((7,3)\)? Wait, no, the end point: when \(t = 7\), \(d=0\)? Wait, the graph shows a line from \((0,0)\) to \((7,0)\)? No, the vertical axis is distance (\(d\)) and horizontal is time (\(t\)). Wait, the graph is labeled "Carlo's Walk" with \(d\) (distance) on the vertical and \(t\) (time) on the horizontal. The line starts at \((0,0)\) and goes to \((7,3)\)? No, the last point: when \(t = 7\), \(d = 0\)? Wait, the grid: each square is, say, 1 unit. So from \((0,0)\) to \((7,3)\)? No, the \(t\) - intercept is at \(t = 7\) and \(d = 0\), and the other end is at \(t = 0\), \(d = 0\)? No, there is a line from \((0,0)\) to \((7,3)\)? Wait, maybe the correct way: The graph has a line from \((0,0)\) to \((7,3)\) (assuming each grid square is 1 unit). Wait, no, the key is:

• Start at the sensor (distance \(0\) m) at \(t = 0\).
• Walk away from the sensor at a constant speed. Let's calculate speed: The change in distance \(\Delta d\) and change in time \(\Delta t\). From the graph, when \(t = 7\) s, \(d=3\) m? Wait, no, the \(t\) - intercept is at \(t = 7\) s and \(d = 0\). Wait, maybe the graph is a line from \((0,3)\) to \((7,0)\)? Oh! I misread the graph. The \(d\) - axis: the top is \(d\) (distance), with \(0,1,2,3,4,5\) and the \(t\) - axis: \(0,1,2,3,4,5,6,7\). The line goes from \((0,3)\) to \((7,0)\)? Wait, the starting point: at \(t = 0\), \(d = 3\) m? No, the graph has a line from \((0,0)\) to \((7,3)\)? No, the user's graph: "Distance (m)" on the vertical, "Time (s)" on the horizontal. The line starts at \((0,0)\) and ends at \((7,3)\)? No, the \(t\) - intercept is when \(d = 0\), so when \(d = 0\), \(t=7\) s. So the line is from \((0,0)\) to \((7,3)\)? No, if \(d = 0\) at \(t = 7\), then the line is from \((0,3)\) to \((7,0)\). Ah, I see, I had the direction wrong. So:

1. Start \(3\) meters away from the sensor at \(t = 0\) (since at \(t = 0\), \(d = 3\) m).
2. Walk towards the sensor at a constant speed. The speed is \(\frac{\text{change in distance}}{\text{change in time}}=\frac{3 - 0}{7-0}=\frac{3}{7}\) m/s.
3. Continue walking towards the sensor until \(t = 7\) seconds, when you reach the sensor (distance \(0\) m from sensor).

So the instructions: Start \(3\) meters away from the sensor. Walk towards the sensor at a constant speed. You should reach the sensor exactly at \(7\) seconds.

Answer:

The \(d\) - intercept is \(0\) m. It means Carlo starts at the sensor's position (distance from sensor is \(0\) m at \(t = 0\)).

Part b)