Motion graphs and acceleration
도입됨| English | 의미 |
|---|---|
| velocity/vəˈlɒsɪti/ | 속도 |
| acceleration/əkˌseləˈreɪʃn/ | 가속도 |
What would explain this observation?
- A speedometer gives a reading at one moment. A journey average can hide stops and rapid changes in speed.
- Start with a prediction. State the quantities or features you would compare, then decide what evidence could distinguish two explanations.
Build the model
- Displacement includes direction; distance counts total path length. Velocity 速度 is change in displacement per time. Acceleration 加速度 is change in velocity per time.
- velocity: Rate of change of displacement; acceleration: Rate of change of velocity.
What does area under a velocity-time graph represent?
난이도 1/5 · 100 코인 + 오늘 첫 완료 시 소액 보너스
Area under a velocity-time graph has units of velocity x time = metres, which is displacement. Acceleration is the GRADIENT of the same graph, and mass does not appear on it at all.
Match each technical term to its precise meaning.
난이도 2/5 · 140 코인 + 오늘 첫 완료 시 소액 보너스
Use the definitions to distinguish related quantities and processes.
Choose evidence that can test it
- The gradient of a displacement-time graph is velocity. The area under a velocity-time graph gives displacement. A constant-acceleration formula is valid only when its assumption is justified.
- Choose a positive direction and state it. Use a light gate or video with a known scale and frame interval for repeatable motion measurements. Avoid assuming hand timing is exact over very short intervals.
Which two habits make the investigation or model in this case more defensible?
난이도 2/5 · 140 코인 + 오늘 첫 완료 시 소액 보너스
Stating the conditions and assumptions lets others repeat the work exactly, and recording the supporting evidence lets them check the conclusion. Hiding disagreeing results removes the evidence that could challenge a wrong conclusion, and one measurement can never establish a wider claim.
Work from known quantities
- State the known values and their units. Choose the relation because its assumptions fit this case, then rearrange before substitution.
- Known: velocity rises uniformly from 2 to 10 metres per second in 4 s. a = (v-u)/t. a = (10-2)/4 = 2 metres per second squared. Displacement is trapezium area: s = (u+v)t/2 = (2+10)×4/2 = 24 m.
Velocity changes from 3 to 15 metres per second in 6 s. Find acceleration. Use the same sequence: known quantities → model → relation → substitution → unit and interpretation.
Velocity changes from 3 to 15 metres per second in 6 s. Find acceleration.
난이도 2/5 · 140 코인 + 오늘 첫 완료 시 소액 보너스
The result is 2 m/s². Known: velocity changes from 3 to 15 metres per second in 6 s. Use a = (v - u)/t. a = (15 - 3)/6 = 2 metres per second squared. The positive sign shows the acceleration is in the direction of motion.
Check the conclusion and its limits
- Negative velocity indicates direction under the chosen sign convention; it does not necessarily mean slowing down.
- Return to the original observation. Explain what the result supports, which conditions it assumes, and one way to test a competing explanation.
A negative velocity always means the object is slowing down. This claim is false: Negative velocity means motion opposite to the chosen positive direction. The object slows down only when the acceleration opposes the velocity; a negative velocity with negative acceleration is speeding up.
Motion graphs and acceleration: The gradient of a displacement-time graph is velocity. The area under a velocity-time graph gives displacement. A constant-acceleration formula is valid only when its assumption is justified.
A negative velocity always means the object is slowing down.
난이도 1/5 · 100 코인 + 오늘 첫 완료 시 소액 보너스
Negative velocity means motion opposite to the chosen positive direction. The object slows down only when the acceleration opposes the velocity; a negative velocity with negative acceleration is speeding up.
Rate of change of displacement: write the technical term.
난이도 1/5 · 100 코인 + 오늘 첫 완료 시 소액 보너스
velocity means Rate of change of displacement.