Area Under The Velocity Graph


In this step, you will graph acceleration versus time, and then calculate the area under that graph at various times. The values of those areas will then be plotted on their own graph in the next step which will be an estimate of distance versus time. This step is virtually identical to the step in which you estimated the area under the deceleration curve except now you're estimating the area under the velocity curve.

You will need to again use the "Area" tool to accomplish this.

In the "Estimate Area Under Curve" window, plot the speed versus time by entering the right hand side of the equation of speed as a function of time (that you found in the last step) in the "y =" text field and then pressing the "Graph Your Equation" button. On this graph, x will again stand for the time variable in seconds.

As you did when finding the area under the deceleration curve, estimate the area under the velocity curve at various times. You may want to use a different shape or shapes (other than a rectangle) to accomplish this.

Since the car's distance at time t = 0 is d = 0, then the area estimates at a particular time are how far the car has travelled in that time.

For example, if you have found that the area at time t = 2.5 is 100, then the car has travelled 100 ft in the 2.5 seconds since the driver has applied the brakes.

After repeating this procedure for various times, you will have a set of points representing an estimate of the car's distance versus time.

Next: Follow the "Distance Curve" link to the left.


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