From middle school math, you may remember that you find the slope by taking the rise over the run. We can calculate the slope of the following graph. The computer calculates the error at every point, and tries to minimize the square of that error. Computers calculate the best fit line using an algorithm called the Least Squares Fit.
In middle school, you may have learned to draw a best fit line by hand using a ruler. This is particularly useful for when there is a lot of noise in our data. In the following graph, you can see an object which is incrementally speeding up. The faster the object goes, the greater the slope of the graph. It is important that when you have a graph, there is a title, axes labels, and units. If the graph is flat or horizontal, then the object is not moving, the slope is zero, and the velocity is zero. The slope of this line will be the average velocity of our object. We generally put position on the y-axis, and time on the x-axis. If we make a graph of position vs time and our object is moving at a constant velocity, the graph will form a straight line. However, if you are working with a weighted average then you cannot use this simple trick by plugging in numbers.Ĭonstant velocity: Position vs Time graph: When you first learned about averages, you probably added two numbers together and divided the result by two.
Contra-wise, If two cars are driving in opposite directions from each other, their relative velocities are the sum of the magnitude of their velocities.Īnother interesting problem you will explore in the homework has to do with finding average speeds. However it seems that they are passing you very slowly. You might be driving at 50 mph, when you are passed by a car driving at 55 mph. Consider when you are driving on the highway. If you were to foolishly walk against the sidewalk, your velocity in the ground’s frame of reference would actually be slow.Īnother example If two cars are driving in the same direction, their relative velocities are the difference of the magnitude of their speeds. When you walk with the sidewalk, your velocity in the frame of reference of the ground is actually faster. In the frame of reference of the moving sidewalk, you are moving at a casual pace. Think of what happens when you step on a moving sidewalk at the airport. Hume for PSSC Physics called Frames of Reference. The question of how velocities are all relative was wonderfully demonstrated in a video from the 1950’s by Dr. Galileo investigated the issue of relative velocities. The direction of the velocity is important, even in the case for one-dimensional motion.
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