Question pattern: Projectile with fluid resistance
Original question 2 of 2 in this pattern
Approach to terminal speed
A small object is released from rest and falls through a fluid. Its downward speed is measured at one-second intervals.
a) Estimate the terminal speed from the data.
b) Describe how the magnitude of the acceleration changes during the fall.
c) Describe the corresponding acceleration–time graph.
d) Explain what happens to velocity and acceleration once terminal speed is reached.
| Time / s | Downward speed / m s⁻¹ |
|---|---|
| 0 | 0.0 |
| 1 | 7.0 |
| 2 | 11.0 |
| 3 | 13.5 |
| 4 | 14.6 |
| 5 | 15.0 |
Worked answer
Solution
- Step 1
The measured speed approaches a limiting value close to
15 m s⁻¹, so the estimated terminal speed is about 15 m s⁻¹ downward. - Step 2
Successive speed increases become smaller: 7.0, 4.0, 2.5, 1.1 and 0.4 m s⁻¹ per second. The acceleration magnitude therefore decreases toward zero.
- Step 3
The acceleration–time graph starts positive in the downward direction and falls smoothly toward zero without becoming negative.
- Step 4
At terminal speed, velocity remains constant and non-zero, while acceleration is zero.
Final answer
Terminal speed ≈ 15 m s⁻¹ downward; acceleration decreases toward zero; at terminal speed the velocity is constant and the acceleration is zero.
Common mistake
Saying that terminal speed is zero because acceleration has become zero.
Concepts tested
- terminal speed
- velocity–time data
- changing acceleration
- qualitative graph
Was this explanation helpful?
Next step