Draw a speed v against time graph by guessing of the values of your trip to school this morning. show how this graph can be used to determine distance

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To draw a speed vs. time graph based on your trip to school this morning, you would first need to estimate your speed at different points during the journey. Remember, speed is defined as the distance covered per unit of time.

Here's a step-by-step guide to creating the graph:

1. Start by selecting a time interval for your graph. Divide the total time of your trip into equal intervals. For example, if your trip took 30 minutes, you could use 5-minute intervals.

2. Estimate your speed for each interval. Think about the speed at which you traveled during each time interval. For instance, if you walked slowly at the beginning, you could estimate a slower speed, and if you ran for a while, you might estimate a higher speed.

3. Plot the estimated speed values on the vertical axis (y-axis) of your graph. Assign a scale to the axis based on your estimates. For example, you could use increments of 5 miles per hour.

4. Plot the time values on the horizontal axis (x-axis) of your graph. Label the axis with the appropriate units, such as minutes or seconds.

5. Once you have marked the speed and time values, connect the individual points with a smooth line. The resulting slope of the line will indicate the change in speed over time.

To determine the distance traveled using the speed vs. time graph, you need to find the area under the line on the graph. Mathematically, the distance is equal to the area under the curve.

To find the distance traveled during a specific time interval, you would need to find the area of the corresponding section on the graph. This can be done by dividing the graphed portion into geometric shapes (such as rectangles or triangles) and calculating their individual areas. Once you have the areas of each section, sum them up to get the total distance.

Keep in mind that the accuracy of your estimates will affect the accuracy of the distance calculation. It is generally better to rely on more precise measurements or use electronic devices, such as a speedometer or GPS, to obtain accurate data for constructing the graph and determining the distance covered.

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