The method and the results are on the kinematics lab. Do the analysis yourself first, then check the answers below.
Quick answer: One-dimensional kinematics describes straight-line motion using position, velocity and acceleration, without asking what causes it. These answers go with the AP Physics 1 lab on kinematics: the graph, the calculations, the uncertainties and the conclusion explained, for all 7 analysis questions.
The model answers use the sample data in the results table. Your own values will differ slightly, but the straight-line shape of the graph and the slope method must be the same. Quote results with the number of significant figures the timing allows.
Level: AP Physics 1 (algebra-based) · Curriculum: AP P1 Unit 1
For constant acceleration from rest, Δx = ½at², so Δx against t² is a straight line through the origin. A straight line is easy to judge by eye and its slope gives a directly, while Δx against t is a curve that cannot be checked as easily. Slope = a/2.
Question 2 A check on the table
Mean = (1.22 + 1.19 + 1.22)/3 = 3.63/3 = 1.21 s. Then t² = 1.21² = 1.464 s², which matches the table.
Half the range is (0.72 − 0.70)/2 = 0.01 s. Percentage uncertainty = 0.01/0.71 × 100 = 1.4 %. Squaring doubles it, so t² has about 2.8 % uncertainty.
Question 5 Prediction
t = √(2Δx/a) = √(2 × 1.50 / 0.82) = √3.66 = 1.9 s.
Question 6 An intercept
A positive t² intercept means the measured time is shorter than expected for a given distance, as if the clock started late or the ball had a small initial push. The ball was not released exactly from rest at the start line, or the stopwatch was started after release. Systematic timing or release error.
Question 7 Improving the method
Use two light gates connected to a timer instead of a stopwatch to remove reaction time, and use more repeats with a longer ramp so the times are larger. Either change lowers the percentage uncertainty. Light gates and longer distances.
