Summary of "[물리1] 1단원 2차시 등속 직선 운동"

Topic

Uniform linear motion (등속 직선 운동) — motion with constant direction and constant speed (uniform velocity).

Linear motion: motion along a straight line (constant direction).
Uniform motion (uniform velocity): constant speed and direction, so velocity is constant.

Axes: vertical = position (s), horizontal = time (t).
For uniform velocity the s–t graph is a straight line.
Slope of an s–t graph:

v = Δs / Δt The slope (Δs/Δt) equals the velocity v (units: m/s).
Examples:
- Turtle: v = 1 m/s → straight line with slope 1 m/s.
- Rabbit: v = 2 m/s → steeper straight line.

Axes: vertical = velocity, horizontal = time.
For uniform motion the v–t graph is a horizontal line at the constant velocity value.
Slope of the v–t graph = change in velocity / change in time = acceleration (here zero).
Area under the v–t graph over a time interval = displacement during that interval. For constant v:

displacement = velocity × time = v × Δt

A negative slope or negative velocity value indicates motion in the opposite direction; the sign of velocity encodes direction.
The magnitude (absolute value) of velocity is speed; comparing magnitudes compares speeds.

Read coordinates from s–t graphs and compute slope: v = (s2 − s1) / (t2 − t1).
Turtle example: moves 1 m every second → v = 1 m/s.
Rabbit example: moves 2 m every second → v = 2 m/s.
Use area under v–t graph to get displacement: area = base (time interval) × height (velocity).
Comparison examples:
- A had v = 1 m/s, B had v = 2 m/s.
- Another example: A = 2/3 m/s and B = −1 m/s (negative indicating leftward motion).
Distance traveled vs displacement: use graph positions to compute change in position; sign gives direction, absolute value gives magnitude traveled in that interval.

Reading a position–time (s–t) graph to find velocity:
- Pick two points on the straight-line segment: (t1, s1) and (t2, s2).
- Compute Δt = t2 − t1 and Δs = s2 − s1.
- Velocity v = Δs / Δt (units: m/s). The sign indicates direction.
Interpreting slope:
- Larger (steeper) positive slope → larger positive velocity (faster to the right).
- Negative slope → motion to the left (velocity < 0).
Reading a velocity–time (v–t) graph:
- For constant velocity, the graph is horizontal at v = constant.
- Slope of v–t = acceleration; for uniform motion slope = 0 (no acceleration).
Finding displacement from a v–t graph:
- For a time interval Δt where v is constant: displacement = v × Δt.
- Geometrically: area under the v–t curve over that interval (rectangle area = base × height).
Comparing speeds and velocities:
- To compare instantaneous velocities at a given time, compare the slopes on the s–t graph or the values on the v–t graph.
- To compare speeds (magnitudes), take absolute values of velocities.
Determining distance traveled vs displacement on s–t graph:
- Displacement over an interval = final position − initial position (signed).
- Distance traveled (if direction changes) = sum of absolute position changes between direction changes; for uniform-direction intervals simply |v| × Δt.

Velocity = slope of s–t, not an angle measure on a ruler.
Area under v–t gives displacement, not instantaneous velocity.
Average speed over an interval = total distance / total time; for uniform motion this equals the constant speed.
Negative velocity means motion in the opposite (conventionally left) direction.