The axes are position and time. Neither is a direction in space, so the line is not a path.
Step 1: Something to Notice
Watch first. The explanation comes later.
A car traveling in a perfectly straight line produces a curved position-time graph. A car going round a bend at constant speed produces a straight one.
How can the graph curve when the road does not, and be straight when it does?
Step 2: Find Out
Isolate each motion and compare the shapes of all three graphs at once.
Step 1 — Predict
A horizontal line on a velocity-time graph means what?
Choose what you think will happen. You cannot see the experiment until you do — guessing first is what makes it worth watching.
Step 3: So Here Is Why
Now the explanation, after you have seen it happen.
Slope of position is velocity
Steeper means faster. A curve means the velocity is changing, whatever the road is doing.
Slope of velocity is acceleration
The same rule one level down. A straight sloping velocity graph is constant acceleration.
Area under velocity is displacement
Rate multiplied by time, which is what an area on this graph is.
A horizontal line means three different things
Not moving, moving steadily, or changing velocity steadily — depending on which graph it is on.
Not a picture of the journey
A rising line on a distance-time graph does not mean going uphill. Students routinely read motion graphs as maps, and correcting that reading is most of what the topic is about.
Slope and area both mean something
On a velocity-time graph the slope is acceleration and the area underneath is displacement. Two different pieces of information sit in the same picture.
Step 4: A Common Mistake
Lots of people think
“A position-time graph shows the shape of the path traveled.”
Step 5: Why the Area Under a Velocity Graph Is the Displacement
The same idea somewhere new.
For constant velocity, displacement is velocity multiplied by time — which is exactly the area of the rectangle under the line. For changing velocity the same holds if you cut the motion into thin strips and add the little rectangles, which is what an integral is. The area rule is not a separate fact to memorize; it is what multiplying rate by time looks like on a graph.
Step 6: Think It Through
Practice makes it stick.
The Curved Graph
Problem 1 of 2
A car drives in a straight line and its position graph curves. Why?
A Flat Line
Problem 2 of 2
A velocity-time graph is a horizontal line at 20 m/s. What is happening?
Reading the Three Graphs
1 of 5
Match each graph feature to what it gives.
Tap a card on the left to start.
2 of 5
What does a curved position-time graph mean?
3 of 5
A horizontal line on a position graph means what?
4 of 5
A horizontal line on a velocity graph means what?
5 of 5
Why is the area under a velocity graph the displacement?
Step 7: Quick Check
Show what you know.
Question 1 of 1
Is a position-time graph a picture of the path?
Step 8: Explain It in Writing
Claim, evidence, then reasoning.
The question
Explain why a position-time graph is not a picture of the path, using a straight road as your case.
Fill in all three boxes. The reasoning box is the one that matters most.
What You Found Out
- The axes are position and time, so the graph is not a map.
- Slope of position is velocity; slope of velocity is acceleration.
- Area under a velocity graph is the displacement.
- A horizontal line means something different on each of the three graphs.