Dueling Buggies Lab (10/8/14)

Partner: Charles Lau
Group 1

Objective Statement:
Our objective was to figure out find out a model which demonstrated at which point two buggy vehicles moving from different directions will meet at. Both buggies moved at different speeds; one moved at a fast constant velocity while the other moved at a slower constant velocity.

Our plan:
1. In order to create the model for our lab, we needed to find the point-intercept equation y=mx+b
2. Our first step was calculating the speeds of both the red buggy - the faster one, and the blue buggy - the slower one
3. We measured out 100 cm on a table and then decided to calculate how long it would take for each each buggy to get across the table from 0 cm to 100 cm.

Data Analysis:
1. We recorded the data of the slow car first. The blue buggy traveled 100 cm in 2.49 seconds
2. Next we recorded the data of the fast car. The red buggy traveled 100 cm in 14.90 seconds.
3. We then calculated the speed of each buggy using the formula speed = distance/time to configure the constant velocities of each car. The blue buggy's slope was 14.90 cm/sec and the red buggy's slope was 40.16 cm/sec  
4. After finding out the slopes of both cars, we proceeded to use our model by setting the red buggy at 0 cm and the blue buggy at 150 cm, which was the given data
5. The equation for the fast red buggy was x = (40.16 cm/sec)t + 0, where t = time and 0 cm = the starting position.excellent!
6. The equation for the slow blue buggy was x = (-14.90 cm/sec)t + 150, where t = time and 150 cm = the starting position. The slope of this equation was negative because the buggy was moving in a negative direction at a slow constant speed.
7. After graphing both equations on a graphing calculator, we discovered that the two buggies intersected at 2.72 seconds when they both reached 109 cm from their opposite starting positions.

Using our Model/Designing a Solution:
With our model, we predicted that the two buggies would meet somewhere between the interval [105 cm, 110 cm] really early into the lab. The fast red buggy's slope was far steeper than the slope of the blue buggy, therefore it would cover more centimeters per second. We also predicted that two buggies would meet somewhere closer to the starting position of the red car rather than near the starting position of the blue one. Our method pretty much synchronized with the data produced, thus we do not believe that it was wrong.  looks great!