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A student carried out an experiment to find the acceleration of a moving trolley - Leaving Cert Physics - Question 1 - 2008

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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 ... 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.

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Answer

To describe the method used to measure the velocity of the trolley, the following steps can be outlined:

  1. Setup the Experiment: Place the trolley on a smooth, straight runway to minimize friction.

  2. Timing Device: Use a timer such as a stopwatch, or a more advanced option like a photogate, to measure the time taken for the trolley to travel a set distance. This timer starts as the trolley is released.

  3. Distance Measurement: Mark a specific distance along the runway where the trolley will travel. It is crucial to measure this distance accurately.

  4. Collecting Data: As the trolley moves past the distance markers, the timing device records the time taken to cover that distance.

  5. Calculating Velocity: Use the formula for velocity, defined as

    v=dtv = \frac{d}{t}

    where v is the velocity, d is the distance traveled, and t is the time taken. This calculation will give the velocity at different time intervals.

  6. Recording Results: Document the velocity measurements at each respective time interval in a table for further analysis.

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).

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Answer

To create a graph of the trolley's velocity against time:

  1. Axes Setup: Draw two perpendicular lines to form the X-axis (horizontal) and Y-axis (vertical). Label the X-axis as "Time (s)" and the Y-axis as "Velocity (m/s)".

  2. Plot Points: Using the data provided:

    • At time 2s, plot the point (2, 0.9).
    • At time 4s, plot the point (4, 1.7).
    • At time 6s, plot the point (6, 2.5).
    • At time 8s, plot the point (8, 3.3).
    • At time 10s, plot the point (10, 4.1) and (10, 4.9).

  3. Fit a Line: Once all points are plotted, draw a line of best fit through the points to illustrate the trend of velocity over time. Ensure that the line extends within the range of the plotted points.

  4. Title the Graph: Add a title to your graph, such as "Velocity vs Time for a Moving Trolley". This will help indicate what the graph represents.

Step 3

Find the slope of your graph and hence determine the acceleration of the trolley.

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Answer

To find the slope of the graph and determine the acceleration:

  1. Select Two Points: Choose two points from the graph to calculate the slope, for instance, (2s, 0.9 m/s) and (10s, 4.9 m/s).

  2. Slope Calculation: Use the formula for the slope, which represents acceleration:

    a=y2−y1x2−x1a = \frac{y_2 - y_1}{x_2 - x_1}

    where:

    • (x1,y1)=(2,0.9)(x_1, y_1) = (2, 0.9)
    • (x2,y2)=(10,4.9)(x_2, y_2) = (10, 4.9)

    Therefore,

    a=4.9−0.910−2=4.08=0.5 m/s2a = \frac{4.9 - 0.9}{10 - 2} = \frac{4.0}{8} = 0.5 \, m/s^2

  3. Conclusion: The calculated acceleration of the trolley is 0.5 m/s².

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