Question

speed and velocity directions: draw a line on each of the time - motion graphs below as instructed. 1. show a car’s constant speed of 75 km/h on a city street. 2. show the motion of a car that travels for 30 seconds on a highway at a speed of 2 km/h, pulls off on the shoulder and stops for half a minute, and then resumes its trip at half its previous speed.

Explanation:

Problem 1: Show a car’s constant speed of 75 km/h on a city street.

Step 1: Understand the graph

The first graph has the y - axis labeled as speed (in km/h, we assume) and the x - axis labeled as time (in minutes). For a constant speed, the graph should be a horizontal line.

Step 2: Locate the speed value

We need to plot a horizontal line at \(y = 75\) (since the speed is 75 km/h) across the time axis (x - axis from 0 to 60 minutes approximately). So, we draw a horizontal line starting from the point where \(y = 75\) on the y - axis and extending along the x - axis for the given time range (0 to 60 minutes).

Problem 2: Show the motion of a car that travels for 30 seconds on a highway at a speed of 2 km/h, pulls off on the shoulder and stops for half a minute, and then resumes its trip at half its previous speed.

Step 1: Analyze the first segment (0 - 30 seconds)

The speed is 2 km/h. On the second graph, the y - axis is speed (let's assume the units are km/h or a scaled version) and the x - axis is time in seconds. We draw a horizontal line at \(y = 2\) from \(x = 0\) to \(x=30\) seconds.

Step 2: Analyze the second segment (30 - 60 seconds)

The car stops, so the speed is 0 km/h. We draw a horizontal line at \(y = 0\) from \(x = 30\) to \(x = 60\) seconds (since half a minute is 30 seconds).

Step 3: Analyze the third segment (60 seconds onwards)

The previous speed was 2 km/h, half of that is \(2\times\frac{1}{2}=1\) km/h. We draw a horizontal line at \(y = 1\) for \(x>60\) seconds.

For the graphical representation:

Graph 1 (Problem 1)

• Y - axis (Speed): Mark 75 on the y - axis (since the y - axis has markings 0, 25, 50, 75, 100).
• X - axis (Time): The x - axis has time from 0 to 60 minutes. Draw a horizontal line parallel to the x - axis passing through the point (0, 75) and extending to (60, 75) (or the end of the time axis on the graph).

Graph 2 (Problem 2)

• First part (0 - 30 s): At \(x = 0\) to \(x = 30\), draw a horizontal line at \(y = 2\) (assuming the y - axis scale, if the y - axis is from 0 to 2, this is the top; if it's a different scale, adjust accordingly).
• Second part (30 - 60 s): At \(x = 30\) to \(x = 60\), draw a horizontal line at \(y = 0\).
• Third part (60 s +): At \(x>60\), draw a horizontal line at \(y = 1\).

(Note: Since the problem is about drawing lines on the graph, the above steps describe how to construct the velocity - time graphs for the given motions. If a numerical answer was expected, but the problem is about graphing, the key is to plot the horizontal lines as described.)

Answer:

Step 1: Analyze the first segment (0 - 30 seconds)

The speed is 2 km/h. On the second graph, the y - axis is speed (let's assume the units are km/h or a scaled version) and the x - axis is time in seconds. We draw a horizontal line at \(y = 2\) from \(x = 0\) to \(x=30\) seconds.

Step 2: Analyze the second segment (30 - 60 seconds)

The car stops, so the speed is 0 km/h. We draw a horizontal line at \(y = 0\) from \(x = 30\) to \(x = 60\) seconds (since half a minute is 30 seconds).

Step 3: Analyze the third segment (60 seconds onwards)

The previous speed was 2 km/h, half of that is \(2\times\frac{1}{2}=1\) km/h. We draw a horizontal line at \(y = 1\) for \(x>60\) seconds.

For the graphical representation:

Graph 1 (Problem 1)

• Y - axis (Speed): Mark 75 on the y - axis (since the y - axis has markings 0, 25, 50, 75, 100).
• X - axis (Time): The x - axis has time from 0 to 60 minutes. Draw a horizontal line parallel to the x - axis passing through the point (0, 75) and extending to (60, 75) (or the end of the time axis on the graph).

Graph 2 (Problem 2)

• First part (0 - 30 s): At \(x = 0\) to \(x = 30\), draw a horizontal line at \(y = 2\) (assuming the y - axis scale, if the y - axis is from 0 to 2, this is the top; if it's a different scale, adjust accordingly).
• Second part (30 - 60 s): At \(x = 30\) to \(x = 60\), draw a horizontal line at \(y = 0\).
• Third part (60 s +): At \(x>60\), draw a horizontal line at \(y = 1\).

(Note: Since the problem is about drawing lines on the graph, the above steps describe how to construct the velocity - time graphs for the given motions. If a numerical answer was expected, but the problem is about graphing, the key is to plot the horizontal lines as described.)