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 graph which was then used to find its acceleration. The table shows the data recorded. velocity m s⁻¹ 0.9 1.7 2.5 3.3 4.1 4.9 time/s 2 4 6 8 10

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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.

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Answer

To measure the velocity of the trolley, the student used a setup that included a trolley and a runway, which the trolley traveled along.

Timing Mechanism: The student employed a timer, such as a ticker timer or a stopwatch, to measure the time taken for the trolley to travel a predetermined distance.
Distance Measurement: The distance was marked on the runway, and a sense of distance was essential for calculating velocity.
Recording Velocity: The velocity was calculated using the formula:

$ext{velocity} = \frac{\text{distance}}{\text{time}}$
Diagram: A diagram should illustrate the setup, showing the trolley, runway, timer, and measurement points, indicating how the measurements were recorded at intervals to find velocity.

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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To create the graph:

Label Axes: The X-axis should represent time (in seconds), while the Y-axis represents velocity (in m/s).
Plot Points: Points should be plotted based on the recorded data:
- (2, 0.9)
- (4, 1.7)
- (6, 2.5)
- (8, 3.3)
- (10, 4.1)
- The maximum velocity is 4.9 m/s at 10 seconds.
Draw the Line: Connect the points with a straight line or curved line that best fits the plotted points, indicating increasing velocity over time. Ensure a neat presentation on graph paper.

Step 3

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

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Answer

To calculate the acceleration:

Identify Two Points: Choose two points from the graph, for example, point 1 at (2, 0.9) and point 5 at (10, 4.9).
Calculate Slope:
- Use the slope formula:
$ext{slope} = \frac{y_2 - y_1}{x_2 - x_1}$

Substituting the values:

$\text{slope} = \frac{4.9 - 0.9}{10 - 2} = \frac{4.0}{8} = 0.5 \text{ m/s}^2$
Acceleration: The acceleration of the trolley is equal to the slope of the velocity vs. time graph, which is 0.5 m/s².

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

Worked Solution & Example Answer:A student carried out an experiment to find the acceleration of a moving trolley - Leaving Cert Physics - Question 1 - 2008

Describe, with the aid of a diagram, how the student measured the velocity of the trolley.

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).

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

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