The method and the results are on the motion graphs lab. Do the analysis yourself first, then check the answers below.
Quick answer: On a distance-time graph the gradient is the speed and a flat line means stopped. These answers go with the grade 8 science lab on motion graphs: the graph, the calculations, the uncertainties and the conclusion explained, for all 7 analysis questions.
Model answers use the sample table. Your own times will differ a little, but you should still find a curved distance-time graph and an acceleration of roughly half a metre per second squared for a gentle ramp.
0–20 cm: 0.20 ÷ 0.90 = 0.22 m/s 20–40 cm: 0.20 ÷ 0.37 = 0.54 m/s 40–60 cm: 0.20 ÷ 0.28 = 0.71 m/s 60–80 cm: 0.20 ÷ 0.24 = 0.83 m/s 80–100 cm: 0.20 ÷ 0.22 = 0.91 m/s
Question 2 Distance-time graph
The points make a curve that gets steeper, so the speed of the ball is increasing as it moves down the ramp.
Question 3 Estimating acceleration
a = change in speed ÷ change in time = (0.91 − 0.22) ÷ (1.90 − 0.45) = 0.69 ÷ 1.45 = 0.48 m/s².
Question 4 Final speed
Average speed = 1.00 ÷ 2.01 = 0.50 m/s. Final speed = 2 × 0.50 = 1.0 m/s. a = 1.0 ÷ 2.01 = 0.50 m/s², close to the estimate in the previous question.
Question 5 Reaction time
0.1 ÷ 0.90 = 11 %. The short early times are affected most, so the early section speeds are the least reliable.
Question 6 Steeper ramp
The curve is steeper and the times are shorter, because a steeper ramp gives a larger acceleration, so the ball gains speed faster.
Question 7 Improvements
Use a phone video with a frame counter, or light gates, to time the ball, and repeat each time more than three times to find a mean. Any two sensible improvements earn full credit.
