Graphing Position-Time graph from a story 1. The car leaves home and travels 40.0 km south in 1.5 hours. 2. The car is stationary for 1.0 hour. 3. The car continues south for 30.0 km. It takes the car 1 hour to travel this distance. 4. The car then turns around and travels 100.0 km

Here's how to graph the position-time graph for the car's journey:<br /><br />**1. Setting up the Graph:**<br /><br />* **X-axis (Horizontal):** Represents time (in hours). Label it "Time (h)".<br />* **Y-axis (Vertical):** Represents position relative to home (in km). Since the car travels south, we'll consider south as the negative direction. Label it "Position (km South)".<br /><br />**2. Plotting the Points and Segments:**<br /><br />* **Segment 1: 40 km south in 1.5 hours:**<br /> * Starting point: (0, 0) (At time zero, the car is at home, which is our reference point).<br /> * Ending point: (1.5, -40)<br /> * Draw a straight line connecting these two points. The slope of this line represents the car's velocity during this period.<br /><br />* **Segment 2: Stationary for 1 hour:**<br /> * Starting point: (1.5, -40)<br /> * Ending point: (2.5, -40) (The time advances by 1 hour, but the position remains the same).<br /> * Draw a horizontal line connecting these points. A horizontal line indicates zero velocity.<br /><br />* **Segment 3: 30 km south in 1 hour:**<br /> * Starting point: (2.5, -40)<br /> * Ending point: (3.5, -70) (The car travels further south, so the position becomes more negative: -40 - 30 = -70)<br /> * Draw a straight line connecting these points.<br /><br />* **Segment 4: 100 km north (back towards home) in an unspecified time:** The problem doesn't state how long this segment takes. Let's assume it takes 't' hours.<br /> * Starting point: (3.5, -70)<br /> * Ending point: (3.5 + t, -70 + 100) = (3.5 + t, 30) (The car travels north, so its position becomes less negative. If it travels far enough north, the position becomes positive).<br /> * Draw a straight line connecting these points. The slope of this line will depend on the value of 't'. A steeper slope means a higher speed.<br /><br /><br />**Key Features of the Graph:**<br /><br />* **Sloping lines:** Indicate motion. The steeper the slope, the greater the speed.<br />* **Horizontal lines:** Indicate that the car is stationary (zero velocity).<br />* **Negative position values:** Indicate the car is south of home.<br />* **Positive position values:** Indicate the car is north of home.<br /><br /><br />**Without the time for the last segment, the graph is incomplete. If you are given the time for the last leg, you can fully plot it. If not, you can just indicate the direction of the line segment (upward and to the right) and label it with "+100 km" to show the change in position.**<br />