Question

SLOPE WALK congratulations the president of the line factory has presented your class with a special challenge she now wants a way to write the equatio of a line generated when a customer walks in front of a motion detector that way a customer can simply walk a line to order it from the factory

Your Task: Once a motion detector has
been set up with the correct software,
have a volunteer walk away from the
motion detector at a constant rate. In
other words, he or she should walk the same speed the entire time. Then, once a
graph is generated, find the equation of the line. Also find the equation of a line
formed when a different volunteer walks toward the motion detector at a constant
rate.

Answer 1

To find the line's equation of a customer walking away or towards a motion detector, calculate the slope using two points and determine the y-intercept. A positive slope indicates walking away, whereas a negative slope indicates walking toward the motion detector.

To find the equation of a line of a customer walking in front of a motion detector, we must calculate the slope using two points on the graph. Let's assume that while analyzing the data, we identify two points: (6.4 s, 2000 m) and (0.50 s, 525 m). The process we'll use involves the following steps:

1. Designate the points as (x1, y1) and (x2, y2), where x represents time and y represents position. In our example, (x1, y1) = (0.50 s, 525 m) and (x2, y2) = (6.4 s, 2000 m).
2. Calculate the slope (m) of the line using the formula slope = (y2 - y1) / (x2 - x1). Using our points, the slope would be (2000 m - 525 m) / (6.4 s - 0.50 s).
3. Substitute the values into the formula to get the slope. Once obtained, use one of the points to solve for the y-intercept (b) using the formula y = mx + b.

If we have a different volunteer walking towards the motion detector, the slope of the line would be negative, since the distance decreases over time as the volunteer approaches the sensor. To find this line's equation, we would follow the same steps as above, using two points from the new graph that the walking motion produces.

In a graphical analysis of one-dimensional motion, a straight line signifies constant velocity, and its slope signifies the speed of the customer walking. The y-intercept would indicate the initial position relative to the detector at the time measuring began.