Motion Graphs Study Notes

Motion is a change in position measured by distance and time.
Distance vs. Displacement:
- Distance: a scalar quantity referring to how much an object has covered during its motion.
- Displacement: a vector quantity referring to the object's overall change in position.
Speed vs. Velocity:
- Speed: tells us the rate at which an object moves.
- Velocity: tells the speed and direction of a moving object.
Acceleration: tells us the rate at which speed or direction changes.
Parts of a Graph: X-axis, Y-axis, Origin, Slope.

Time is always plotted on the X-axis.
Distance is plotted on the Y-axis.
The slope of the distance-time graph indicates the velocity of the object.
Speed on a distance-time graph is read from the slope: steeper slope = higher velocity.

At Rest: Time increases to the right, distance does not change (horizontal line).
Constant Speed: Distance increases linearly with time (straight line with constant slope).
Increasing Speed: Line becomes steeper over time (curve upwards if acceleration is changing; a curved line with increasing slope shows acceleration).
Higher Steepness: A steeper line indicates a larger distance moved in a given time, i.e., higher speed.
Constant vs. Accelerated Motion:
- Constant speed: straight line (constant slope).
- Accelerated motion: curve that becomes steeper (increasing slope).

Slope formula: $\text{Slope} = \frac{yf - yi}{xf - xi} = \frac{\Delta d}{\Delta t}.$
Implications:
- Steep slope = higher velocity.
- Shallow slope = lower velocity.

The steeper the graph, the faster the motion.
A horizontal line means the object is not changing its position — at rest.
A downward-sloping line indicates the object is returning to the start (note: this is typically discussed in the context of displacement-time graphs; distance-time graphs do not decrease distance).

Example scenario: A graph where distance is plotted and a line slopes downward would indicate returning toward the start if interpreted as displacement-time.
When comparing two runners starting at different positions:
- A graph with one runner starting 10 yards ahead is reflected by the vertical separation between the lines at any given time.
- If two runners have the same slope, they are moving at the same speed; if slopes differ, their speeds differ.

Which graph shows one runner starting 10 yards ahead?
In which graphs are both runners moving at the same speed?
These questions use the relative positions and slopes of lines to infer starting points and speeds.

Match descriptions to graphs:
1. The car is stopped.
2. The car is travelling at a constant speed.
3. The speed of the car is decreasing.
4. The car is coming back.
Graph A, B, C, D correspond to these descriptions; explanations rely on whether the line is flat, rising steeply, curving upward, or curving downward.

Time is always plotted on the X-axis.
Speed or Velocity is plotted on the Y-axis.
A straight horizontal line means speed is constant (not changing over time).
Important: A straight line does not mean the object is not moving; it means the speed is constant.

Increasing speed (accelerating): the graph shows a rising line with positive slope.
Decreasing speed (decelerating): the graph shows a falling line with negative slope.
If two objects are compared on a speed-time graph:
- Both lines may increase in speed, but the line with greater acceleration reaches top speed faster.
- The dashed vs. solid lines can indicate different accelerations even if final speeds are the same.

Average velocity for an accelerating object is given by the average of the initial and final velocities:
- $V = \frac{vi + vf}{2}.$
Note: Velocity is the speed in a particular direction. Velocity can be computed as $V = \frac{d}{t}.$

Given various graphs with segments E–H, match to descriptions:
- 5. The car is stopped.
- 6. The car is travelling at a constant speed.
- 7. The car is accelerating.
- 8. The car is slowing down.
Each graph segment corresponds to the described motion based on whether the line is horizontal, rising, or falling.

Distance-time graphs: slope = velocity; steeper slope means faster motion; horizontal line means rest.
Speed-time graphs: horizontal line means constant speed; rising line indicates acceleration; falling line indicates deceleration.
Velocity is a vector quantity; speed is a scalar.
Displacement accounts for direction; distance does not.
Average velocity for constant acceleration is the average of initial and final velocities: $V = \frac{vi + vf}{2}.$

Graphs translate real-world motion into visual trends: starting position, speed changes, stops, and direction changes.
Understanding slope and area under speed-time graph (not explicitly covered here) can extend to distance traveled; here the focus is on slope and qualitative trends.

Distance is a scalar; Displacement is a vector.
Time axis on x-axis; Distance axis on y-axis for distance-time graphs.
Speed-time graphs place speed on the y-axis with time on the x-axis; horizontal = constant speed.
Slope signifies rate of change: on distance-time graphs, slope = velocity; on displacement-time graphs, slope = velocity as well.
Typical motion categories: rest, constant speed, accelerating, decelerating, uniform motion vs. accelerated motion.