(Solved): How can I write a formula using that information? 2.1.2 Determining a constant acceleration model ...

How can I write a formula using that information?

2.1.2 Determining a constant acceleration model Overview of the experiment - You will drop a cylinder, length \( \mathrm{L} \), through the plastic tube of the free fall apparatus. The cylinder will start from rest at the top of the tube. (Be sure to drop the cylinder from the same starting point each time.) The photogates will be positioned some distance, \( h \), apart. The top photogate (gate 1) should be positioned 10-15 centimeters from the top of the plastic tube and the bottom photogate (gate 2) about 30 centimeters below the top photogate. When you drop the cylinder, with length \( l \), through the tube, it will accelerate and pass through both photogates. Each photogates will collect data on how long it takes the falling cylinder to pass through the gate, \( t_{1} \) for the top gate and \( t_{2} \) for the bottom gate. The software also gives the time for the cylinder to travel between the two photogates as \( t \). 2.1.3 Developing the mathematical model Using the time intervals, \( t_{1} \) and \( t_{2} \), for the cylinder to break the beam for each photogate and the length of the cylinder, \( l \), write an expression for the initial velocity (through gate 1) and the final velocity (through gate 2 ) for the cylinder as it falls. Using some combination of the distance, \( h \), both the initial and final velocities, the time between gates, and the acceleration constant, \( a \), write a useful constant acceleration expression to represent a mathematical model of the falling cylinder. Keep in mind how information is extracted from a graph and what your goal of the experiment is. Be sure to check that the units on each side of the equation match.