solve---**Question Stem:**
12. Find the speed of the object in this graph:
**Chart/Diagram Description:**
* **Type:** 2D Cartesian coordinate graph, specifically a distance-time graph.
* **Main Elements:**
* **Coordinate Axes:**
* **X-axis (Horizontal):** Labeled "time (s)". The scale starts at 0 and extends to at least 15. Major tick marks are labeled at 0, 5, 10, and 15. There are 5 minor grid divisions between each major tick, indicating that each minor division represents 1 second.
* **Y-axis (Vertical):** Labeled "distance (m)". The scale starts at 0 and extends to at least 100. Major tick marks are labeled at 0, 20, 40, 60, 80, and 100. There are 2 minor grid divisions between each major tick, indicating that each minor division represents 10 meters.
* **Data Series (Curve):**
* A single, thick black curved line is plotted on the graph.
* The curve originates from the origin (0,0).
* It continuously increases in both time and distance, extending into the first quadrant.
* The curve is concave up, meaning its slope is continuously increasing as time progresses.
* Approximate data points on the curve:
* At time = 0 s, distance = 0 m
* At time = 5 s, distance is approximately 4-5 m.
* At time = 10 s, distance is approximately 20 m.
* At time = 15 s, distance is approximately 68-70 m.
* **Grid:** A regular grid of horizontal and vertical lines corresponds to the major and minor tick marks on both axes.
**Options:**
a. At 7 seconds
b. At 11 seconds
c. At 13 seconds
d. Is the object moving forwards or backwards?
e. Is the object accelerating or decelerating?
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Distance-time graphs are fundamental tools for analyzing motion. The horizontal axis represents time in seconds, while the vertical axis shows distance in meters. The key insight is that the slope of the line represents the object's speed. A steeper slope indicates higher speed, while a horizontal line means the object is stationary. For a straight line, we have constant speed, calculated as the change in distance divided by the change in time.
Now let's examine the specific graph from our problem. The curve starts at the origin and passes through several key points: approximately 7.5 meters at 5 seconds, 30 meters at 10 seconds, and 67.5 meters at 15 seconds. Notice that this is not a straight line, but a curved line that bends upward. This upward curvature, called concave up, is crucial because it tells us that the slope of the line is continuously increasing. Since slope represents speed, this means the object is accelerating - its speed is getting faster over time.