Quick answer: One-dimensional kinematics describes straight-line motion using position, velocity and acceleration, without asking what causes it. This AP Physics 1 lab on kinematics gives the aim, the equipment, the safety points, a step-by-step method, sample results and 7 analysis questions; the answers are on a separate page and the lab sheet is a free printable PDF.
How can you prove that a ball rolling down a ramp has a constant acceleration, and measure it with a stopwatch and a ruler? In this lab you time the ball over five distances, convert the times to t², and use a straight-line graph of distance against t² to find the acceleration and its uncertainty.
Level: AP Physics 1 (algebra-based) · Curriculum: AP P1 Unit 1
Aim
To measure the constant acceleration of a ball rolling from rest down a ramp, and to show that the displacement is proportional to t².
Equipment
- smooth straight board or track, about 1.3 m long
- books to raise one end by a few centimetres
- steel ball or marble
- metre rule and marker
- stopwatch (a phone timer is fine)
Safety
Place a tray or a stop block at the bottom of the ramp so the ball cannot roll across the floor. Pick up any ball that lands on the ground at once so nobody slips on it.
Method
- Mark a start line near the top of the ramp and mark points 0.20, 0.40, 0.60, 0.80 and 1.00 m below it.
- Release the ball from rest at the start line, without pushing it.
- Start the stopwatch at release and stop it when the ball passes the first mark.
- Repeat three times for this distance and record all three times.
- Repeat for each of the other marks, keeping the ramp angle fixed.
- Calculate the mean time and t² for each distance.
Results
Sample measurements:
| Δx (m) | t₁ (s) | t₂ (s) | t₃ (s) | mean t (s) | t² (s²) |
|---|---|---|---|---|---|
| 0.20 | 0.72 | 0.70 | 0.71 | 0.71 | 0.504 |
| 0.40 | 1.02 | 1.00 | 1.01 | 1.01 | 1.020 |
| 0.60 | 1.22 | 1.19 | 1.22 | 1.21 | 1.464 |
| 0.80 | 1.43 | 1.41 | 1.42 | 1.42 | 2.016 |
| 1.00 | 1.58 | 1.55 | 1.58 | 1.57 | 2.465 |
Analysis questions
Question 1 Why plot against t²
Explain why plotting Δx against t² is better than plotting Δx against t.Question 2 A check on the table
Use the three times for Δx = 0.60 m to confirm the mean time and t² in the table.Question 3 Finding the acceleration
Use the first and last rows to find the slope of the Δx–t² graph and calculate the acceleration.Question 4 Timing uncertainty
The three times for 0.20 m range from 0.70 s to 0.72 s. Estimate the uncertainty in the mean time and its percentage uncertainty.Question 5 Prediction
Use your acceleration to predict the time for the ball to travel 1.50 m from rest.Question 6 An intercept
Another group finds that its best-fit line crosses the t² axis at a positive value instead of passing through the origin. Suggest a reason.Question 7 Improving the method
Propose two changes to the set-up that would make the measured acceleration more precise, and say why each helps.
