In physics, any increase or decrease in velocity is referred to as acceleration or deceleration. The rate of acceleration is measured in m/s² or km/m/s respectively. The average acceleration of an object can be derived from the formula:
To identify the correlation between the movement of the cart and the appearance of the velocity time-graph and use that correlation to calculate the displacement and acceleration of the cart.
Controlled Variable: the ramp, the timer, the cart releaser, the testing environment, length of ticker tape, the angle of the ramp
Independent: The average velocity of the cart per interval
Dependent: The total displacement of the cart
1) A table was drawn to record time, displacement and average velocity.
2) The ramp, recording timer and cart was set up in the test environment.
3) A length of recording tape was attached to the cart and threaded through the ticker timer.
4) The timer was started and the cart was released down the ramp so that the recording tape was pulled through the timer.
5) Steps 3 and 4 were repeated until each person in the group had a tape of the motion.
6) The marking tape was analyzed by marking the starting dot t= 0 and dividing the tape into equal time intervals. Each six dot interval was .10s.
7) The displacements of each time interval were recorded in the table.
8) The average velocity was calculated and recorded for each time interval.
9) The graph of the velocity for the cart was plotted at the half time intervals.
10) The line of best fit was drawn through the points.
11) The average acceleration of the cart were calculated by finding the slope of the velocity- time graph in m/s²
|Time Interval (s)|
Average Velocity Per Interval
|Time Elapsed (s)||Distance per Interval (m) [fwd]||Average Velocity (m/s) [fwd]|
Average Velocity Overall (Total Displacement)
|Time Elapsed (s)||Total Distance (m) [fwd]||Average Velocity (m/s) [fwd]|
|Average Velocity for Entire Trip: 1.17 (m/s) [fwd]|
Average Change in Velocity (Acceleration)
|Time Interval (s)||Average Velocity (m/s)||Acceleration (m/s²) [fwd]|
|Average Acceleration for Entire Trip: 2.4m/s²|
After performing the experiment four times there are several conclusions that can be drawn from it; the first of which being errors.
Equipment Error: During the experiment there were difficulties that sometimes occurred with the ticker tape timer. Though the machine worked quite effectively the problem was encountered with the purple carbon disc that created imprints on the ticker tape paper. During the experiment on two occasions the disc would either not imprint anything on to the ticker tape paper or come off during that experiment. This resulted in trails having to be repeated and the waste of lab materials to retrieve accurate data.
Inherent Error: There’s always potential for inherent errors during an experiment and this one is not an exception. The cart being released and the operation of the ticker tape timer were done by two different group members. This created the possibility for the cart to be released slightly before or after the ticker tape timer was activated. Though it may not seem drastic because the time measurements being recorded are so miniscule such a synchronization problem can significantly change in average velocities per interval.
There are two major improvements that can be proposed to make the data collected from this experiment more precise and accurate. The first improvement would be the creation of a tool to allow one person to operate both the ticker tape timer and release of the car. By creating a release button that would operate both devices it would synchronize them and ensure the data was precise. Also placing groove on the board which the car could run along on the ramp would allow the car to have a constant start and end track on the board. This would eliminate the variation of places the car could start and finish from and the chance of the car falling of the board near the end of its run.
1) The average velocity for an interval can be found by finding the slope of that interval. Using the tangent method or mid-point method to find the rise/run will give you the average velocity of the cart at that interval.
2) For constant acceleration, the average velocity for the interval will be equal to the instantaneous velocity at the half-time of the interval.
3) The average velocity for an interval on a velocity- time graph must be plotted on one specific point on the line to represent instantaneous velocity.
4) If the acceleration is constant, then the velocity-time graph will be a linear line. However if the acceleration deviates positively then the velocity-time graph will gain a curved or parabolic shape.
5) Based of the data from the velocity time graph, the cart is experiencing non-uniform motion.
6) The average acceleration of the cart is 2.4m/s² or 240cm/s².
7) The area underneath the each interval was the relatively the same as the displacement of the cart at that interval. It should however be exactly the same as the displacement of the cart at the interval. The values may be different simply due to rounding during the calculations.
a) To create a velocity-time graph from a position – time graph divide the displacement of each interval by the time at of each interval; the resultant will be the average velocity of each interval. Then plot that average velocity as the dependent variable on a velocity-time graph; plot time as the independent variable.
b) To create a position- time graph from a velocity- time graph find the average velocity of each interval. (This can be done through finding the slope of each interval) Then multiply each average velocity by its time interval to get the displacement. Then plot each displacement value in accordance with its time interval on a position-time graph.
c) To create an acceleration- time graph from a velocity time graph find the slope of each interval. Once the average acceleration (slope) of each interval is calculated, plot each average acceleration value with its appropriate time interval.
d) To create a velocity- time graph from an acceleration- time graph find the average acceleration of each time interval. Then multiply the average acceleration with the time interval to get the average velocity and plot it with its corresponding time interval.
10) The ticker tape cart experience uniform acceleration and had a constant magnitude 2.4m/s² [fwd] down the ramp.
In conclusion, the velocity time graph of the cart down the ramp had a relative, if not completely linear shape. To determine the displacement of the cart, find the area underneath the line of the velocity-time graph and to find the acceleration of the cart, find the slope of the line of the velocity-time graph. The data collected from this experiment was quite accurate and testing was performed quite smoothly, however as stated early, there is always room for improvement.