SkarpChapter 9 of 14
Describing Motion: Distance, Speed, and Graphs
Whether it is a car on the highway or a falling ball, motion leaves a mathematical trail—learn to read and sketch the stories hidden in simple motion graphs.
Step 1 – What Does It Mean to Describe Motion?
What is Describing Motion?
Describing motion means answering: Where is an object, how is its position changing, and how fast is that change happening? Physics uses clear definitions so everyone means the same thing.
Key Ideas We Use
To describe motion, we use: reference point and position, distance vs. displacement, speed and average speed, velocity, acceleration, and distance–time graphs.
Why This Matters
These ideas are not just school concepts. In 2026, engineers and scientists still use them for car safety systems, sports analysis, and planning space missions. You are learning their basic language.
Step 2 – Reference Point and Relative Motion
Reference Point
A reference point is a fixed place you compare positions to. Position is where an object is relative to that reference point, like “200 m east of my house.”
Relative Motion
Motion depends on the observer. On a train, your backpack seems still to you, but a person on the platform sees it moving. Both are correct because they use different reference points.
Choosing a Reference
In everyday problems, we usually choose the ground, a building, or a starting line as the reference point. Always be clear about what you are measuring motion relative to.
Step 3 – Distance vs. Displacement
What is Distance?
Distance is the total ground covered. It is always positive and has no direction. Example: walking 500 m, no matter which way you turn, adds to your distance.
What is Displacement?
Displacement is the straight-line change from start to finish, including direction, like “20 m east.” It can be zero even when you have moved a lot.
Comparing the Two
Walk 60 m east, then 40 m west: distance = 100 m, displacement = 20 m east. On a full 400 m track lap, distance = 400 m, displacement = 0 m.
Step 4 – Practice: Distance vs. Displacement
Scenario Overview
A student walks 30 m north to the library, 30 m south back to the entrance, then 10 m south to the bike rack. Take north as positive and the entrance as position 0.
Calculating Distance
Add all path lengths: 30 m north + 30 m south + 10 m south = 70 m. Total distance walked is 70 m.
Calculating Displacement
Positions: start 0 m, then +30 m, then 0 m, then -10 m. Displacement = final − initial = -10 m, or 10 m south of the entrance.
Step 5 – Speed, Average Speed, and Velocity
Average Speed
Average speed = total distance ÷ total time. It tells you how fast you covered the whole trip, not every moment-by-moment change.
Units and Example
Common units are m/s and km/h. Example: 6 km in 20 min → 20 min = 1/3 h, so average speed = 6 ÷ (1/3) = 18 km/h.
Speed vs. Velocity
Speed has no direction. Velocity adds direction, like “18 km/h north.” Changing direction, even at the same speed, means your velocity has changed.
Step 6 – A Qualitative Look at Acceleration
What is Acceleration?
Acceleration describes how velocity changes. Speeding up, slowing down, or changing direction all count as acceleration.
Everyday Examples
Starting from a stoplight (speed increases), braking to stop (speed decreases), or turning sharply at steady speed are all examples of acceleration you can feel.
Key Idea
Modern devices measure acceleration in m/s², but for now remember: any change in velocity, not just speed, means there is acceleration.
Step 7 – Reading Distance–Time Graphs
Axes of a Distance–Time Graph
On a distance–time graph, time is on the horizontal axis and distance from a reference point is on the vertical axis.
Lines and Motion
Flat (horizontal) line: not moving. Straight sloping line: constant speed. Steeper line: faster speed.
Curves and Acceleration
A curve getting steeper means speeding up. A curve getting less steep means slowing down. In all cases, the slope of the graph tells you about speed.
Step 8 – Describe the Motion from Graph Stories
Imagine these three distance–time graphs. For each, describe the motion in words.
- Graph A
- From 0 to 5 s: a straight line going up evenly from 0 m to 20 m.
- From 5 to 10 s: a flat horizontal line at 20 m.
Your task: Describe what the object is doing from 0–5 s and 5–10 s.
- Graph B
- A straight line from 0 m at 0 s to 50 m at 10 s.
- Graph C is steeper: from 0 m at 0 s to 50 m at 5 s.
Your task: Compare the speeds in Graph B and Graph C. Which is faster and why?
- Graph C (curved)
- Starts at 0 m.
- The curve rises slowly at first, then becomes steeper and steeper up to 10 s.
Your task: Explain how the speed is changing over time.
Pause and answer in your own words before checking typical answers:
- Graph A: Moving away at constant speed for 5 s, then stopped at 20 m.
- Graph B vs C: C is faster because the same distance is covered in less time (steeper line → higher speed).
- Graph C (curved): The object is speeding up; distance increases more quickly as time passes.
Step 9 – Quick Check: Average Speed and Graphs
Test your understanding of average speed and reading distance–time graphs.
A runner's distance–time graph is a straight line from 0 m at 0 s to 100 m at 20 s. What is the runner's average speed?
- 2 m/s
- 4 m/s
- 5 m/s
- 20 m/s
Show Answer
Answer: A) 2 m/s
Average speed = total distance ÷ total time = 100 m ÷ 20 s = 5 m/s? Careful: 100 ÷ 20 = 5, but units: 100 ÷ 20 = 5, not 2. The correct math is 100 ÷ 20 = 5, so the correct answer is 5 m/s. (Check: 5 × 20 = 100.)
Step 10 – Quick Check: Distance vs. Displacement
Test your understanding of distance and displacement.
A hiker walks 3 km east, then 1 km west. Which statement is correct?
- Distance = 2 km, displacement = 4 km east
- Distance = 4 km, displacement = 2 km east
- Distance = 2 km, displacement = 2 km east
- Distance = 4 km, displacement = 4 km east
Show Answer
Answer: B) Distance = 4 km, displacement = 2 km east
Total distance = 3 km + 1 km = 4 km. Net change from start: 3 km east − 1 km west = 2 km east, so displacement = 2 km east.
Step 11 – Flashcard Review
Flip these cards (mentally or with a partner) to review key terms from this module.
- Reference point
- A fixed place used to describe position and motion, e.g., your house, the starting line, or the ground.
- Distance
- The total path length an object travels, always positive and without direction.
- Displacement
- The straight-line change in position from start to finish, including direction (a vector).
- Speed
- How fast distance changes; distance traveled per unit time, without direction.
- Average speed
- Total distance divided by total time for a trip.
- Velocity
- Speed with direction; how fast displacement changes (a vector).
- Acceleration
- How velocity changes over time, including speeding up, slowing down, or changing direction.
- Distance–time graph
- A graph with time on the x-axis and distance on the y-axis, used to describe motion; the slope represents speed.
Step 12 – Apply It: Create Your Own Motion Story
Now connect everything by creating your own motion story.
- Pick a situation
- Example: walking from your room to the kitchen, or a bus trip from home to school.
- Describe the path in words
- Where do you start (reference point)?
- Do you stop anywhere?
- Do you ever turn around or go back?
- Estimate numbers
- Distances for each part of the path (in m or km)
- Times for each part (in s or min)
- Calculate
- Total distance
- Displacement from start to finish (with direction)
- Average speed for the whole trip
- Sketch a distance–time graph
- Time on the x-axis, distance from your starting point on the y-axis
- Use flat sections for stops, straight sloping lines for constant speed
Challenge yourself to explain your graph to someone else using the words: distance, displacement, speed, velocity, acceleration, and reference point.
Key Terms
- speed
- How fast distance changes; distance traveled per unit time, without direction.
- distance
- The total length of the path an object travels, regardless of direction.
- position
- An object's location relative to a chosen reference point, often given with a direction.
- velocity
- Speed in a particular direction; how fast displacement changes.
- acceleration
- The rate at which velocity changes over time, including changes in speed or direction.
- displacement
- The straight-line change in position from start to end, including direction.
- average speed
- Total distance traveled divided by the total time taken.
- reference point
- A fixed place used to describe where an object is and how it moves relative to that place.
- slope (of a graph)
- How steep a line is on a graph; on a distance–time graph, the slope represents speed.
- distance–time graph
- A graph showing how an object's distance from a reference point changes over time, with time on the horizontal axis and distance on the vertical axis.