Unit 3 Constant Acceleration

In Unit 3, we placed a cart on a ramp that was set at an angle and measured its position on the track after we released it from the top of the ramp.  We also had the option of using a 1 in steel sphere instead of the cart.  We had to mark its position at a set time interval using a dry erase marker and then measure its position away from the beginning.  When we graphed the data, we noticed that we got a parabolic curve.  We used a graphing utility such as LoggerPro or Plotly or Excel to come up with an equation for the graph.  We noticed that when we used a steeper ramp that there was a larger coefficient to the equation.  We were asked why the graph was parabolic and we noticed that when we doubled the time, we quadrupled the position. 

Then we looked at the relationship between velocity and time and we noticed that we had a linear relationship here.  When we compared the coefficients of the position vs time graph with the velocity vs time graph, the coefficients appeared to double. 

So we looked at the model so far, by looking at the motion map for carts on a ramp with velocity and acceleration arrows and we had noticed that the velocity increased while the acceleration remained constant.  We noticed that with constant acceleration, the position - time graph was a parabolic shape and the velocity - time graph was linear and the acceleration - time graph was constant. 

We did another lab where we collected data where different groups had their carts go up or down the ramp with either positive or negative velocities and let the cart come back down.  We noticed a relationship between acceleration and velocity.  See following picture.

Then we looked at a scenario where the steel sphere went down a ramp onto a flat surface and noticed that it accelerated down the ramp and when with a constant velocity along the flat surface.  We looked at the corresponding graphs.  We looked at how the area under a velocity - time graph was the displacement of the object and used the graph to develop a math model for displacement.  We collected data using different scenarios with the carts down a ramp and found that the values of the acceleration, initial velocity and displacement matched up nicely to the equations.

We then dropped a bean bag onto the motion detector to determine what the free-fall acceleration actually meant.  We came up with a value that was pretty close to 9.8 m/s/s and we were comfortable with using 10 m/s/s as the value for future use.