Plot a distance- time graph of the tip of the second hand of a clock b...
Introduction:
A distance-time graph represents the distance traveled by an object over a period of time. In this case, we will plot the distance traveled by the tip of the second hand of a clock over one minute.
Given Information:
- Circumference of the circle traced by the second hand = 64cm
Plotting the Graph:
- We will select four points on the x-axis and y-axis respectively to plot the graph.
- The x-axis represents time in seconds, and the y-axis represents distance in cm.
- Since the second hand completes one revolution in 60 seconds, the distance traveled in one second will be equal to the circumference of the circle traced by the second hand divided by 60.
- We will calculate the distance traveled by the second hand at every 15 seconds and plot the graph accordingly.
Table of Values:
| Time (sec) | Distance (cm) |
|------------|---------------|
| 0 | 0 |
| 15 | 16 |
| 30 | 32 |
| 45 | 48 |
| 60 | 64 |
Plotting the Points:
- We will plot the points (0,0), (15,16), (30,32), (45,48), and (60,64) on the graph.
- We will join the points with a straight line to obtain the distance-time graph of the tip of the second hand of a clock.
Conclusion:
- The distance-time graph of the tip of the second hand of a clock shows that the distance traveled by the tip of the second hand is directly proportional to the time elapsed.
- The slope of the graph represents the speed of the second hand.
- The distance traveled by the tip of the second hand in one minute is equal to the circumference of the circle traced by the second hand, which is 64cm.
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