One-Dimensional Motion: Valid vs Invalid Graphs
This simulation demonstrates proper one-dimensional motion graphs and shows invalid cases that cannot represent physical motion.
Invalid Graph Examples
Graph (a): Position vs Time (Invalid)
Observation: The curve loops back on itself.
Issue: At a given time t, there are multiple positions x.
Reasoning: A particle can't be in two places at once.
Issue: At a given time t, there are multiple positions x.
Reasoning: A particle can't be in two places at once.
✅ Verdict: Cannot represent 1D motion
Graph (b): Velocity vs Time (Invalid)
Observation: Closed circular loop.
Issue: For a given t, two velocity values exist.
Reasoning: A particle can't have two velocities at once.
Issue: For a given t, two velocity values exist.
Reasoning: A particle can't have two velocities at once.
✅ Verdict: Cannot represent 1D motion
Graph (c): Speed vs Time (Invalid)
Observation: Curve dips below zero.
Issue: Speed is negative.
Reasoning: Speed is always ≥ 0 (magnitude of velocity).
Issue: Speed is negative.
Reasoning: Speed is always ≥ 0 (magnitude of velocity).
✅ Verdict: Cannot represent 1D motion
Graph (d): Path Length vs Time (Invalid)
Observation: Path length decreases.
Issue: Total distance can't decrease.
Reasoning: Path length is cumulative distance.
Issue: Total distance can't decrease.
Reasoning: Path length is cumulative distance.
✅ Verdict: Cannot represent 1D motion
Valid One-Dimensional Motion
Position vs Time (Valid)
Observation: Single-valued function.
Property: Each t maps to exactly one x.
Reasoning: Correct representation of position.
Property: Each t maps to exactly one x.
Reasoning: Correct representation of position.
Valid 1D motion
Velocity vs Time (Valid)
Observation: Single-valued function.
Property: Each t maps to exactly one v.
Reasoning: Correct representation of velocity.
Property: Each t maps to exactly one v.
Reasoning: Correct representation of velocity.
Valid 1D motion
Speed vs Time (Valid)
Observation: Always non-negative.
Property: |v| ≥ 0 at all times.
Reasoning: Correct representation of speed.
Property: |v| ≥ 0 at all times.
Reasoning: Correct representation of speed.
Valid 1D motion
Path Length vs Time (Valid)
Observation: Never decreases.
Property: Monotonically increasing.
Reasoning: Correct representation of distance.
Property: Monotonically increasing.
Reasoning: Correct representation of distance.
Valid 1D motion
Value: 1 m/s
Value: 0 m/s²
Key Principles of One-Dimensional Motion
- Position-Time Graph: Must be single-valued (vertical line test). A particle cannot be in two places at the same time.
- Velocity-Time Graph: Must be single-valued. A particle cannot have two velocities simultaneously.
- Speed-Time Graph: Must always be non-negative. Speed is the magnitude of velocity.
- Path Length-Time Graph: Must be non-decreasing. Distance traveled cannot decrease over time.
