Above is the diagram, data points collected, and the processed graphs of time vs position and time vs velocity, respectively.
A definition of the problem and selection of variables
How does time affect the position and velocity of a cart on a ramp?
Independent variable: time
Dependent variable: position
The controlling variables
Using the laptop allowed for a still camera, head on the cart. This made for lack of shaking of the camera or warped perspectives. We also used one cart, for one trial to prevent any differences across data points.
A developed method for the collection of data
The video of the cart going down the ramp was imported to Logger Pro 3.15. Logger Pro can track the motion of the cart and gather data on its position over time, and from there, velocity can be calculated via the clicking of the cart on the video frame by frame.
The procedure
A ramp was propped up onto a metal elevation device. The ramp contained grooves designed to keep the cart in place. One person filmed the event from a head-on angle. One person released the cart while someone at the end caught it once it left the ramp. A meter stick was left in view for reference of length. There was one recorded trial.
Graphs and graphical analysis
x(t)= -0.3304t^2 + .4140t - 0.04101
The graph is concave down and parabolic. The slope of this position-time graph is becoming steeper in a negative direction, meaning the velocity is becoming more negative. Since the sign is negative, the cart is moving in a negative direction. The y-intercept is the initial position and the slope is velocity.
v(t)= -0.7162t + 0.5012
The graph is linear and decreasing. The slope of this velocity-time graph is negative and constant, meaning that the acceleration is negative and constant. Because the sign of velocity matches that of the acceleration, the cart is speeding up as time increases. The initial velocity is the y-intercept.
Conclusion
As time increased, the position of the cart decreased parabolically. This can be compared, on a more macroscopic scale, to the position of a car as it is rolling down a hill, or really any object rolling at a downward angle. As time increased, and the cart rolled down the ramp, velocity became more negative and more negative. Since the slope of this time vs velocity graph is negative, the acceleration is also negative. Thus the cart is speeding up as time increases because the signs for a(t) and v(t) match each other. We are fairly confident in our data considering our enormous amount of data points. However, only one trial was completed using a camera that was not the best that may have warped the perspective to some extent. It is also possible that the releaser of the cart added some force before pushing it downwards, adding additional speed to the data. To improve, the data could be collected with a better camera like one with a tripod. There could have been a robot releasing the cart to completely minimize the chance that any force was put on the object. Repeated trials could have been done to get more graphs and more data, allowing for more accuracy of position against time with this cart specifically.
A definition of the problem and selection of variables
How does time affect the position and velocity of a cart on a ramp?
Independent variable: time
Dependent variable: position
The controlling variables
Using the laptop allowed for a still camera, head on the cart. This made for lack of shaking of the camera or warped perspectives. We also used one cart, for one trial to prevent any differences across data points.
A developed method for the collection of data
The video of the cart going down the ramp was imported to Logger Pro 3.15. Logger Pro can track the motion of the cart and gather data on its position over time, and from there, velocity can be calculated via the clicking of the cart on the video frame by frame.
The procedure
A ramp was propped up onto a metal elevation device. The ramp contained grooves designed to keep the cart in place. One person filmed the event from a head-on angle. One person released the cart while someone at the end caught it once it left the ramp. A meter stick was left in view for reference of length. There was one recorded trial.
Graphs and graphical analysis
x(t)= -0.3304t^2 + .4140t - 0.04101
The graph is concave down and parabolic. The slope of this position-time graph is becoming steeper in a negative direction, meaning the velocity is becoming more negative. Since the sign is negative, the cart is moving in a negative direction. The y-intercept is the initial position and the slope is velocity.
v(t)= -0.7162t + 0.5012
The graph is linear and decreasing. The slope of this velocity-time graph is negative and constant, meaning that the acceleration is negative and constant. Because the sign of velocity matches that of the acceleration, the cart is speeding up as time increases. The initial velocity is the y-intercept.
Conclusion
As time increased, the position of the cart decreased parabolically. This can be compared, on a more macroscopic scale, to the position of a car as it is rolling down a hill, or really any object rolling at a downward angle. As time increased, and the cart rolled down the ramp, velocity became more negative and more negative. Since the slope of this time vs velocity graph is negative, the acceleration is also negative. Thus the cart is speeding up as time increases because the signs for a(t) and v(t) match each other. We are fairly confident in our data considering our enormous amount of data points. However, only one trial was completed using a camera that was not the best that may have warped the perspective to some extent. It is also possible that the releaser of the cart added some force before pushing it downwards, adding additional speed to the data. To improve, the data could be collected with a better camera like one with a tripod. There could have been a robot releasing the cart to completely minimize the chance that any force was put on the object. Repeated trials could have been done to get more graphs and more data, allowing for more accuracy of position against time with this cart specifically.