Acceleration is the time rate of change of velocity, am = Av/At. If an object which is moving in a straight line undergoes equal changes in velocity in equal intervals of time, it is said to be moving with uniform or constant acceleration. For constant acceleration, the average acceleration is the same as the instantaneous acceleration. A constant net force on an object produces constant acceleration. The earth's force of gravity is nearly constant near the surface of the earth. Therefore, objects moving only under the force of gravity will be uniformly accelerated. The relationship between speed, time, and acceleration at two different points when the object travels with constant acceleration is thus given by v = vO + at Eq. I where v = velocity at time t and v0 is its velocity at time t = 0, or the initial velocity. Thus for uniform acceleration, there is linear relationship between speed and time, which means that a speed versus time graph will be a straight line. The slope of that line is the acceleration 'a,' and the 'v' intercept is the initial speed, v0. When the speed varies linearly with time, the average speed during any time interval is equal to the instantaneous speed at the midpoint of the time interval. The equation describing the position (X) of an object moving with uniform acceleration is X:XO+VOt+l/20t2 Eq.2 where x0 = initial position (m) of the object at time t = 0 s, v0 = initial velocity (m/s), and a = uniform acceleration (I'D/32) PROCEDURE: 1. If you have not done so already, download a free copy of the Graphical Analysis software at mp3://Www.vernier.com/product/gmphical-analysis-4/ 2. Review how to use the Graphical Analysis software. There are several YouTube videos on how to use this software. Here is one that will get you going: h_ttps://www.youtubecom/watch? v=ngvL4j0a2d0. As with learning anything, the more you use it or play with it, the more skillful you become, so explore its use as much as possible. It will come in handy. 3. Using the simulation atmps://www.g@gebra.org/m/evbtuer, click the start button to drop the ball and to obtain data of the position of the falling object as a function of time in the spreadsheet. 4. Select and copy the data from the spreadsheet and paste in the data table in Graphical Analysis. 2. Plot v vs. t (be sure to label appropriately with correct units) using Graphical Analysis Software. Copy and paste it below. From equation 1 on the instruction sheet, what kind of graphical fit do you expect for a v vs. t graph 3. Choose the appropriate curve fit, and obtain the initial speed v, and the acceleration a from the results of your curve fit. 4. The accepted value of 'g' = 9.8 m/s (980 cm/s). Calculate your percent error. Also do a percent difference between the initial speed obtained from the speed v. time graph and that obtained from the position vs. time graph. Part III: Average Speed 1. From the distance vs. time graph, pick any three consecutive times, t,, t,, and t,. Find the average speed between t, and t, (X, - X,)/(t, - t,), show sample calculation and record it in the table below. Repeat the process for another set of three equally separated times, by finding the average speed between the two end point times and compare with the instantaneous speed at the mid-point time. Trial 12 Vaverage instantaneous 2. What do you observe? Could you have used this method to obtain the instantaneous speed vs. time graph? 3. Compare the average speed obtained above with the instantaneous speed at to, by doing a percent difference calculation. QUESTIONS: 1. Rain clouds form at a height of about 2,000 m above the ground. Under "Free Fall", why would it be dangerous to walk outside when it rains? Back your answer with some basic calculations 2. If the object in the experiment had been given an initial downward push, would the value of g' be different? Explain. 2MOTION WITH CONSTANT ACCELERATION PURPOSE: 1. To understand the concept of velocity and uniform acceleration from the motion of a freely falling object. 2. To plot graphs from simulated \"free fall\" data and to interpret those graphs. 3. To obtain value of gravitational acceleration, 'g.' Interactive Simulation to be used: mp3://www.ggebraorg/m/evbtup Software to be used: Graphical Analysis\Lab 3 Free Fall Data Sheet Name: Date: Use the following link to complete the lab activity. Interactive Simulation to be used:mpI/gWWW.gB_Qgl1fa.l' rn/evlztuer Part I: Distance Time Graph 1 . Plot the data using Graphical Analysis Software. Label your axes distance, with unit, an, on the y axis and time, with unit, 5, on the x axis. Do a quadratic curve t. Compare the curve t equation with Eq 2 on the instruction sheet. Front the comparison, determine the initial velocity v\