Ticker Tapes

Key Question: What is the relationship between position and time for a cart rolling down a ramp? What is the relationship between velocity and time for a cart rolling down a ramp?

Investigating:

                           

     

Explanation- The ticker timer uses a carbon fiber to show the change in velocity over time by creating ticks. The ticker timer makes 6 ticks per 1/10 of a second. We attached a piece of paper to the back of a cart and put the other end through the ticker timer so we can see the marks it makes and measure the velocity change in the cart as the time increases. The cart travels at a downward slope so it gradually speeds up. This is shown by the dots getting further and further apart since they are marked at even time intervals. Using the ticks, we were able to create data to turn into a graph. To make this data, we counted every 6 dots because that represents a tenth of a second. At every 6th dot we measured how far it is from the first dot. By doing that we were able to tell how far the cart traveled at every tenth of a second.  good

Data Analysis: 

Time (seconds)	Position (centimeters)
0.1 seconds	1.5 centimeters
0.2 seconds	4 centimeters
0.3 seconds	7.3 centimeters
0.4 seconds	11.5 centimeters
0.5 seconds	16.5 centimeters
0.6 seconds	22 centimeters
0.7 seconds	28.5 centimeters
0.8 seconds	35.5 centimeters
0.9 seconds	43.2 centimeters
1.0 seconds	52 centimeters
1.1 seconds	61.2 centimeters
1.2 seconds	71.5 centimeters
1.3 seconds	82.3 centimeters

Verbal Model: As the time increases, the position increases at an increasing rate. 

Math Model: x=(38cm/s^2)t^2 

Description: The cart is moving with an increasing velocity in a positive direction.

Velocity vs. Time Graph

Verbal Model: As the time increases, the velocity increases proportionally.
Math Model: Vf=at+Vi       

                        a=(cm/s)/s
Slope: Acceleration ((cm/s)/s or cm/s^2)
Y-Intercept: The initial velocity 

excellent
  Models:

• The new equation for the Position vs. Time graph is Δv x=(1/2)at^2. In this equation Δv  xis the area under the curve. This area represents the total distance traveled during the total amount of time. The new equation of the velocity graph is Vf=at+Vi. This is the derivative of the position graph and allows us to find the velocity equation. "a" represents acceleration, "t" represents time, "Vf" represents the final velocity and "Vi" represents the initial velocity. 

why is this font so weird??  and where did we get these equations - how do they relate to what you saw in lab?

Explaining: 

• No, the numbers for the constants and slopes were different for each group. This is because every group used a different ramp, so each group had a different incline. This causes the constants and slopes to be different because the car sped up at different rates, depending on the steepness of the incline.
• Errors in my experiment could have included using the dots either at the very beginning of the tape or at the very end. This could have messed up my data because during those times, the car wasn’t moving the way it was supposed to. We could have started the timer before we let the car go or stopped the timer after we already slowed down the car, messing up the distance between the dots, which shows how far the car traveled for that certain 
• Another idea to test regarding acceleration is the opposite of this. Instead of speeding up, what if the car was slowing down. Or another experiment could be to use the same ramp with the same incline but add weight to the car to test how weight affects the acceleration. both good ideas