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

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.

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:

   $a = \frac{y_2 - y_1}{x_2 - x_1}$

   where:

   • $(x_1, y_1) = (2, 0.9)$
   • $(x_2, y_2) = (10, 4.9)$

   Therefore,

   $a = \frac{4.9 - 0.9}{10 - 2} = \frac{4.0}{8} = 0.5 \, m/s^2$

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