Movement of the Disc

Conclusion: In conclusion the purpose of this lab was to see how far the rolling disk traveled in different time intervals. The motions studied were the speed of the disk and the position it, when it was stopped after a certain amount of time. The motion map shows hot the velocity is changing and how acceleration remains the same. For example, from 0-5s it traveled 9cm, and from 5-10s it traveled from 18cm.

When the data was plotted in an x-t graph it resulted in a top opening parabola. In order to linearize it, the x-intercept values,(clock reading) had to be squared and once they were plotted into a x-t^2 graph, it resulted in a linear graph. The math model for the x-t^2 graph was x=(0.18 (m/s)⁄s)t^2. There was no y-intercept because due to the 5% rule, when the y-intercept was divided with the greatest y-value the value was less the 5% and therefore, there was no y-intercept. In order to find the tangents of the x-t graph we had to choose around five points from the line, but not the data points and then find the slope of the tangent where we had to divide displacement by the time interval, ∆x/∆t. The slope of a tangent to a point on the parabola curve is instantaneous velocity(v ̅) at an instant in time.. After we got the points we plotted them into an instantaneous velocity vs. clock reading (v-t) graph. The slope for the v-t graph means rate of change of velocity per change in clock reading. The math model of the v-t graph is V=(0.358(m/s)⁄s)t. Also, the slope of a v-t graph is twice of the slope of a x-t^2 slope. Last, acceleration is the rate of change of velocity as a function of time.