Pair+A

Dylan and Elena
 * Crash Course Lab**

1. 2 cars (one fast, one slow) 2. Spark Timer 3. Ticker tape 4. Meter stick
 * Materials for both experiments:**


 * Experiment 1:**

1. We placed the two cars 6 m apart and facing each other 2. We started them at the same time 3. We recorded when the two crashed 4. Then we measured how far each car traveled
 * Procedure:**

**Hypothesis:** The purpose of this experiment is to analyze velocity in a few different ways and  to see how position and time are are used to calculate it. We thought that the Ticker Tape for each car would show dots separated by a constant distance, with the faster car's dots farther apart then the slower car's dots. We also predicted that the pos ition vs. time graph of each car would be a strait line, with a positive slope, with the faster car's slope more steep, then the slower car's.

For this experiment, we set up the cars exactly 600 cm or 6 m apart, one at each end of the measuring tape. CMV (constant moving vehicle 1) was our fast car, which from our ticker tape experiment, had an almost constant velocity of .3006 meters per second. CMV 2 was our slow car which had an constant velocity of .1145 m per second. We started the cars at the same exact time. By careful observation, we noticed that the cars crashed about 2.04 meters from where the slower car started. That meant that the fast car traveled about 3.96 m. However, to solidify our observations, we did some calculations to find the exact place the cars met:

Fast Car: .3006 m/s Slow Car: .1145 m/s

.3006 m/s + .1145 m/s = .4151 m/s __.3006 m/s__ = .7242 travel 3.96 meters .4151 m/s

.66 x 6.00 m = 3.96 m that the fast car traveled

6.00 m – 3.96 m = 2.04 m that the slow car traveled

It took the slow car about 14 .45 seconds to travel 2.04 m and crash into the fast car. It took the fast car about 14.47 seconds to travel and crash into the slow car.


 * Experiment 2:**
 * Hypothesis:** The fast car will eventually pass the slow car even though the slow car started 1.6 cm ahead of the fast car. The fast car will pass the slow car because it has a greater velocity.

1. We attached each car to a spark timer. 2. We placed the slow car 1.6 cm in front of the fast car. 3. We turned both on an let then run for 2 seconds. 4. We measured the distance between the dots on the spark tape. 5. We recorded and graphed tout data below. 6. With our data we calculated how long it took the fast car to pass the slow one (see calculations below).
 * Procedure:**

Data:

Position Time Graph
 * Time || Distance of slow car || Distance of fast car ||
 * 0 || 1.6cm || 0 ||
 * 0.1 || 3.3cm || 2 ||
 * 0.2 || 5cm || 4 ||
 * 0.3 || 6.7cm || 5.8 ||
 * 0.4 || 8.3cm || 8 ||
 * 0.5 || 9.4cm || 9.9 ||
 * 0.6 || 11.1cm || 11.8 ||
 * 0.7 || 12.7 cm || 13.9 ||
 * 0.8 || 14.6cm || 15.7 ||
 * 0.9 || 16.5cm || 17.7 ||
 * 1 || 17.9 cm || 19.8 ||
 * 1.1 || 19.8cm || 21.9 ||
 * 1.2 || 21.1cm || 23.8 ||
 * 1.3 || 22.7 cm || 25.7 ||
 * 1.4 || 24.3 cm || 27.8 ||
 * 1.5 || 25.6 cm || 29.9 ||
 * 1.6 || 27.7cm || 31.6 ||
 * 1.7 || 29.1 cm || 33.6 ||
 * 1.8 || 30.9 cm || 35.6 ||
 * 1.9 || 32.6 cm || 37.5 ||
 * 2 || 34.4 cm || 39. ||
 * Calculations:**

CMV2 d=1.98t CMV1= d=1.62t+1.6cm

1.98t=1.62t+1.6 .36t=1.6 t=4.44 seconds It took 4.44 seconds for the fast car to pass the slow car.

CMV2=1.98(4.44)=8.79 cm The fast car traveled 8.79 cm before it passed the slow car.

CMV1=1.62(4.44)+1.6=7.66 cm The slow car traveled 7.66 cm before it was passed by the fast car.

Percent error: (2.49-2.04)/2.49 =.18 <span style="font-family: Arial,Helvetica,sans-serif; font: normal normal normal 12px/normal Helvetica; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;">.18(100)=18% error


 * Discussion Questions:**


 * 1.** The slope of the position time-graph is equal to the average velocity. This is because average velocity is the change of distance divided by the change in time. The slope of a line is equal to the change in y-values divided by the change in x-values. So on the graph the position is on the y axis and the time is on the x-axis. Therefore when we find the slope of our line we are actually finding the average velocity.


 * 2.** It is ok to set the y-intercept to zero because that is the starting point of our experiment. We started at time 0 and the position of our car started at 0. Because we start at (0,0) it makes sense to set the y-intercept equal to 0. Also, because we know that we are going to have straight line we know that there will only be one y-intercept and it will be at 0.


 * 3.** The r-squared value tells us how close our data is to its trend line or line of best fit. If the r-squared value was 1 we would know that our graph exactly matched the predicted graph. Our r-squared value was .9999 so we know that the graph we got is accurate because it is essentially equal to one.

4. The cars would meet at the mid point of the distance traveled if their speeds were exactly equal. The midpoint of our lab is 300 cm so that is where they would meet if they had the same speed.

5.) They are at the same place where the two lines intersect. This point is approximately (5.6 tenths of a second, 9)

6.) Yes because this graph provides constant velocity and time. With this data you can find Distance (position) with the equation v=d/t. If you solve for d and set the two equations equal to each other, you can find the position at which they meet.


 * Conclusion:**

<span style="font-family: Arial,Helvetica,sans-serif;">Our hypothesis was correct because the fast car passed the slow car even though the slow car started 1.6 cm ahead of the fast one. We predicted that the fast car would travel farther than the slow one in the same amount of time. From our calculations above we can conclude that it took 4.44 tenths of a second for the fast car to pass the slow one. We got that the fast car traveled 8.79 cm and the slow car traveled 7.19 cm in that time. This supports our hypothesis because we said that the fast car would travel farther this makes sense because the fast car had a higher velocity so it will go farther in the same amount of time as the slow one. <span style="font-family: Arial,Helvetica,sans-serif;"> We calculated the percent error using the equations above and got a 18% percent error. This is a pretty substantial amount of error. Our error came from the precision of the tools that we used. We used a meter stick to measure the distance of the cars but if we used something with smaller measurements like millimeters our results would have been much more exact and our error would have been less.Even though we did a couple trials we still could have had human error with our reaction times and in our readings of the exact point of when the fast car passed the slow one.