Constant acceleration with initial velocity opposite to the direction of acceleration (toss the ball in the air)

For this experiment, start the can at the end of the track nearest the sonic ranger with the fan thrust pointing towards the sonic ranger. Turn on the fan and use two fingers to give the cart an initial velocity that is opposite to the direction of the fan thrust. Give the cart an initial velocity that is sufficient for the cart to move almost half way down the track before stopping, turning around and returning back to its original position. This will likely require some practice runs to get used to the amount of force required to launch the car down the track. The point where the cart velocity is zero and turns around is called a turning point of the motion, and is an important concept in mechanics. This is the same kind of position vs. time motion that happens when you toss a ball vertically upwards in the air. it reaches its maximum height, which is a turning point, reverses velocity, and then returns to its initial position when you catch the ball at the same height it was released from.

Once you get the technique of imparting an initial velocity to the cart, take screenshots of data recorded for two different initial velocities and corresponding maximum distances from the sensor. The two different values of vo should he such that one of the values results in the can taming around slightly less than half way down the track. and the other value of v₀ should be sufficient so that the car makes it nearly to the end of the track before turning around (3/4 of the way down minimum). Make sure that the position vs. time data are smooth and do not have artifacts due to the way you launched the carts. Make screenshots of your data for each of the two different initial velocities and paste them into Word.

a) Was the acceleration constant for the two different vo values? Determine the region where it was constant and report the average values of the acceleration. Compare these values to the acceleration you found in part 2. What do you expect the relationship between the three values to be? Do your results agree with what you expect?

b) From the velocity vs. time graphs, locate the position of the turning point (i.e. the corresponding time). Find the position of the cart at this value of the time and record it for both of your v₀ values. Also record the v₀ values. From the v₀ and values, determine a formula for the expected position of the distance away from the release point where the cart turns around.               

Using the values for v₀ and a that you determined and your formula, calculate the position of the turning point of the cart for the two different initial velocities. Compare these values with the measured values. Make a little table with the various values of v₀, a, x_tp(expt.), x_tp(calc.), where x_tp is the turning point distance from where the cart was initially released. Are the values in approximate agreement?

c) Lastly, note that your graph of position vs. time is a parabola (at least it should be if you took the data correctly), thus one dimensional motion with constant acceleration is sometimes called parabolic motion, even though it is only one dimensional.