The method and the results are on the suvat equations lab. Do the analysis yourself first, then check the answers below.
Quick answer: The suvat equations connect displacement, initial velocity, final velocity, acceleration and time for motion in a straight line with constant acceleration. These answers go with the Physics 11-12 lab on suvat equations: the graph, the calculations, the uncertainties and the conclusion explained, for all 8 analysis questions.
With the sample data the acceleration is close to 0.79 m/s², slightly below the frictionless value of 0.82 m/s². Your own ramp will give a different value, but a straight line through the origin confirms constant acceleration.
Level: Physics grades 11-12 (A Level · IB · Class 11-12) · Curriculum: A Level 3.4, IB A.1
From s = ½at² the graph is a straight line through the origin with gradient ½a.
Question 2 Gradient
Gradient = (1.00 − 0) ÷ (2.53 − 0) = 0.395 m/s².
Question 3 Acceleration
a = 2 × gradient = 2 × 0.395 = 0.79 m/s².
Question 4 Speed at the bottom
v = at = 0.79 × 1.59 = 1.26 m/s. Check: v² = 2as = 2 × 0.79 × 1.00 = 1.58, so v = 1.26 m/s.
Question 5 Theory comparison
Ideal a = 9.81 × (0.10 ÷ 1.20) = 0.818 m/s². Difference = (0.818 − 0.79) ÷ 0.818 = 3.4 % lower than ideal, which is explained by friction and rolling resistance.
Use a light gate or frame-by-frame video to improve timing, and repeat each timing more times to average out random errors. Keep the starting release identical each time.
Question 8 Hypothesis check
From 0.20 m to 0.40 m the time rose from 0.71 s to 1.02 s, a factor of 1.4, not 2. The claim is false: time is proportional to √s, since s ∝ t².
