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A student carried out an experiment to find the acceleration of a moving trolley - Leaving Cert Physics - Question 1 - 2008
Question 1
A student carried out an experiment to find the acceleration of a moving trolley. The student measured the velocity of the trolley at different times and plotted a g... show full transcript
Worked Solution & Example Answer:A student carried out an experiment to find the acceleration of a moving trolley - Leaving Cert Physics - Question 1 - 2008
Step 1
Describe, with the aid of a diagram, how the student measured the velocity of the trolley.
Answer
To measure the velocity of the trolley, the student used a trolley on a runway. A timer, such as a digital stopwatch or a motion sensor, was involved in the experimental setup. The process was as follows:
- Setup: The trolley was placed on a smooth runway to reduce friction.
- Timing System: The student utilized a timer that was either a ticker timer or a datalogger connected to a sensor that measures distance traveled.
- Measurement: The student released the trolley, and as it traveled a known distance, the timer recorded the time taken to cover that distance.
- Calculation: Velocity was calculated using the formula: ext{Velocity} = rac{ ext{Distance}}{ ext{Time}}
- Diagram: A diagram showing the trolley on the runway, timer positioned, and sensor details would help illustrate this process.
Step 2
Using the data in the table, draw a graph on graph paper of the trolley’s velocity against time. Put time on the horizontal axis (X-axis).
Answer
To plot the graph of the trolley’s velocity against time:
- Axes Setup: Start by labeling the horizontal axis as 'Time (s)' and the vertical axis as 'Velocity (m/s)'.
- Points from Data: Plot the points using the provided table data:
- (2, 0.9)
- (4, 1.7)
- (6, 2.5)
- (8, 3.3)
- (10, 4.1)
- (10, 4.9)
- Connecting Points: Connect the plotted points with a straight line, as the graph should be linear, indicating uniform acceleration.
- Best Fit Line: If using graph paper, ensure the points form a straight line; if needs adjusting, draw the best fit line through the points.
Step 3
Find the slope of your graph and hence determine the acceleration of the trolley.
Answer
To find the slope of the graph, we can use two points from our plotted graph. Let’s use the points (2, 0.9) and (10, 4.9):
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Calculate the slope (m) using the formula: m = rac{y_2 - y_1}{x_2 - x_1} where and .
Substituting the values: m = rac{4.9 - 0.9}{10 - 2} = rac{4.0}{8} = 0.5 ext{ m/s}^2
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Determine acceleration: The slope of the velocity-time graph represents the acceleration of the trolley. Therefore, the acceleration of the trolley is: