Question

bubble tube reflection
find the speed of the bubble in each of your two tubes by finding the slope of your graph. use any two points that are on your line of best fit (the farther apart, the better). show your work!
color of tube: green
(2.6,10) (8.6,30)
\\(\frac{30 - 10}{8.6 - 2.6}=\frac{20}{6}\text{ cm/s}\\
color of tube: blue
(2.3,15) (4.4,30)
\\(\frac{30 - 15}{4.4 - 2.3}=\frac{15}{2.1}\text{ cm/s}\\
what would your graphs look like if the bubbles were speeding up? what if the bubbles were slowing down? remember that a large slope on a position - time graph represents a fast speed, and a small slope represents a slow speed.
based on the shapes of your graphs, were the bubbles moving at constant speed or changing speed? explain how your graph provides evidence for your claim.

Explanation:

Step1: Analyze speed - up graph

If the bubbles were speeding up, the position - time graph would be a curve with an increasing slope. This is because as time goes on, the distance traveled in each unit of time (speed) is getting larger.

Step2: Analyze slow - down graph

If the bubbles were slowing down, the position - time graph would be a curve with a decreasing slope. As time progresses, the distance traveled in each unit of time is getting smaller.

Step3: Analyze constant - speed graph

If the bubbles were moving at a constant speed, the position - time graph would be a straight line. This is because the ratio of the change in position to the change in time (slope, which represents speed) is constant. In the given work for green tube ($\frac{30 - 10}{8.6 - 2.6}=\frac{20}{6}$ cm/s) and blue tube ($\frac{30 - 15}{4.4 - 2.3}=\frac{15}{2.1}$ cm/s), if the graph is a straight - line for each tube, it indicates constant speed. If the graph is a curve, it indicates changing speed.

Answer:

If speeding up: Curve with increasing slope.
If slowing down: Curve with decreasing slope.
If constant speed: Straight - line. Evidence: A straight - line graph has a constant slope (ratio of change in position to change in time), while a non - straight (curved) graph has a changing slope, indicating a change in speed.