A student released a trolley from the top of a ramp of length of about 1.5 m, as shown - Edexcel - A-Level Physics - Question 16 - 2023 - Paper 1

Plotting a graph of h against $v^2$ will yield a straight line because the equation $h = \frac{v^2}{2g}$ is a linear relationship. Here, h is directly proportional to $v^2$, meaning that as $v^2$ increases, h increases proportionally. The slope of the graph will be equal to $\frac{1}{2g}$, which is a constant.

The graph should have h (in cm) on the y-axis and $v^2$ (in m$^2$s$^{-2}$) on the x-axis. To plot the graph:

1. Calculate $v^2$ for each corresponding h accordingly:

   • For h = 10.8 cm, $v^2 = (1.38)^2 = 1.9044$ m²/s².
   • For h = 18.9 cm, $v^2 = (1.98)^2 = 3.9204$ m²/s².
   • For h = 28.7 cm, $v^2 = (2.45)^2 = 6.0025$ m²/s².
   • For h = 40.3 cm, $v^2 = (2.86)^2 = 8.1796$ m²/s².
   • For h = 49.8 cm, $v^2 = (3.22)^2 = 10.3684$ m²/s².
   • For h = 58.7 cm, $v^2 = (3.46)^2 = 11.9936$ m²/s².

2. Make sure to label the axes correctly, using suitable scales, and plot the calculated points accurately. Finally, draw a straight line of best fit through the points.

The student's conclusion about her value for g being consistent with the accepted value should be evaluated with respect to the precision of her measurements and the potential for systematic errors in her experimental setup. If the graph shows a straight line that closely follows the theoretical values, it indicates that her results are likely valid. However, discrepancies may arise from factors such as friction, measurement errors, or inaccuracies in the timing, which should be acknowledged.