Motion graphs and acceleration
導入済み| English | 意味 |
|---|---|
| velocity/vəˈlɒsɪti/ | 速度 |
| acceleration/əkˌseləˈreɪʃn/ | 加速度 |
What would explain this observation?
- A speedometer gives a reading at one moment. A journey average can hide stops and rapid changes in speed.
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?
難易度 1/5 · 100 コイン + 今日初回完了時に小ボーナス付与
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.
難易度 2/5 · 140 コイン + 今日初回完了時に小ボーナス付与
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.
In the lab: 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?
難易度 2/5 · 140 コイン + 今日初回完了時に小ボーナス付与
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
- 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.
Your turn: Velocity changes from 3 to 15 metres per second in 6 s. Find acceleration.
Velocity–time: displacement and distance
$v=u+at;\quad s=ut+\frac12at^2$
Signed area gives displacement; total absolute area gives distance.
Velocity changes from 3 to 15 metres per second in 6 s. Find acceleration.
難易度 2/5 · 140 コイン + 今日初回完了時に小ボーナス付与
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.
Not true: A negative velocity always means the object is slowing down. 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.
- Displacement includes direction; distance counts total path length.
- The gradient of a displacement-time graph is velocity.
- Watch for: negative velocity indicates direction under the chosen sign convention; it does not necessarily mean slowing down.
Write from an acceleration of 4 metres per second squared
- Velocity rises uniformly from 4 to 16 metres per second in 3 s.
- Find the acceleration and the displacement. A negative velocity means the opposite direction.
A negative velocity always means the object is slowing down.
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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.
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velocity means Rate of change of displacement.
Velocity rises uniformly from 4 to 16 metres per second in 3 s. What are the acceleration and the displacement, and what does a negative velocity mean?
Acceleration is the change in velocity divided by time. Displacement for uniform acceleration is the average velocity times time.
What is the acceleration?
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(16 minus 4) divided by 3 is 4 metres per second squared. The 30 m figure is the displacement. Other options — 2 metres per second squared (the worked acceleration); 30 m (the displacement).