Dueling Buggies Lab

Objective Statement
The problem we were trying to solve was to come up with a way where we could calculate where the two cars, with different velocities, coming from opposite directions would meet. To find out the position and the time of the collision, we needed to either come up with an algebraic equation or solve it graphically. To do so, we needed to collect our measurements and calculate the different variables that would make up the formula needed to solve our problem.

Your Plan

What we did was we found the average velocities of both of the buggies. Because one was faster than the other, we ran 2 trials.

1. Aligned 2 rulers after each other, with the overall length of 80 inches. 
2. Marked every 10 inches the rulers.
3. Placed the buggy at 0 inches. 
4. Once the buggy would start traveling, we started the stopwatch.
5. With the stopwatch, we timed how many seconds it took for the buggy to reach the markings at 10 inches. 
6. After recording down the relatively close times, we calculated the average of all of them (7-8 for each buggy) to get the most legitimate time. 
7. Plugged our results into Velocity=Distance/Time formula to calculate speed. 
8. Repeated the process for the 2nd buggy. 

To calculate the average, we added all of the time measurements together and divided by how many measurements there were recorded. To convert our sec per 10 inches to velocity, we divided the time by distance. By doing so, we found the rate for both of the buggies.
Calculations
1st buggy
10in/1.84sec= 5.43in/sec

2nd buggy
10in/0.46sec=21.74in/sec
distance/time = speed ... I need to see those calcualtions

From the data we collected, it was evident that the 2nd buggy was much faster than the 1st buggy because it took the 2nd buggy 4 times as fast to reach the 10 inches compared to the 1st buggy. 

Data Analysis

After a long time of not figuring out how to connect the information to solve our problem, we finally reached a conclusion. Since the problem included rate, time, and distance, it occurred to me that we could use the rate times time = distance formula. Therefore I tried an equation we usually see in our math books in a word problem: (rate and time of the first buggy) plus (the product of rate and time of the second buggy) which would equal the overall distance. With the lab, the equation looked a little like this: (5.43t)+(21.7t)=the given distance.  Adding these 2 equal the total distance because the amount they both traveled equal the total distance. (5.43t) is the amount of distance the first buggy traveled, and (21.7t) is the amount the second buggy traveled until the collision. You need the total distance to calculate the collision point. WHY does adding these 2 equal the total distance...  this is important to explain - 5.43 is the rate of the first, slow buggy, while 21.7 is the rate of the faster buggy. 

ok good!  :)

Buggy #1	Buggy #2
1.90 sec/10 in	0.38 sec/10 in
1.95 sec/10 in	0.41 sec/10 in
1.68 sec/10 in	0.40 sec/10 in
1.9 sec/10 in	0.48 sec/10 in
1.76 sec/10 in	0.52 sec/10 in
1.93 sec/10 in	0.55 sec/10 in
=1.83 sec/10 in	=0.46 sec/10 in

Model/Designing a Solution

With our formula, we would be solving how many seconds it would take for the two buggies to collide. With the given distance of 65, we plugged it into the equation                 (5.43t)+(21.7t)=65 to get an answer of 2.4 seconds. Then, we ran a trial run with the stopwatch and it took exactly 2.4 seconds for the cars to collide at 17.5 inches, meaning our method was successful.