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š¬ From table to line
Given a table of positions at different times, how do we turn it into a graph step by step?
How do we plot a position-time graph?
- Draw two perpendicular lines meeting at the origin O: horizontal X-axis (time), vertical Y-axis (position).
- Choose a convenient scale for each axis (e.g. X: 5 divisions = 1 s; Y: 5 divisions = 20 m).
- Mark each (time, position) pair as a point, then join the points. For the data in Table 4.3 the points fall on a straight line .
Important Definitions
- Origin (O) — the point of intersection of the two perpendicular axes from which values are measured.
- X-axis and Y-axis — the horizontal line (here, time) and the vertical line (here, position) used to plot the graph.
- Scale — the chosen relation between graph divisions and the quantity (e.g. 5 divisions = 1 s), picked to use the space conveniently.
ā Note
- All the graphs in this chapter are for motion in a straight line in one direction only . In this case distance = magnitude of displacement and speed = magnitude of velocity.
- If position is zero at time zero, the position-time graph is the same as the distance-time graph, and the velocity-time graph is the same as the speed-time graph.
ā Note
- A graph is not a route map . It does not show the route taken, only how the position of the object changes with time with respect to the origin.
š¹ Ready to Go Beyond — intermediate points
- The intermediate points on the line represent possible positions at in-between times. They are correct only if the vehicle is moving at a constant speed .
| Time | 0 s | 1 s | 2 s | 3 s | 4 s | 5 s | 6 s |
|---|---|---|---|---|---|---|---|
| Position | 0 m | 20 m | 40 m | 60 m | 80 m | 100 m | 120 m |
In this Activity, we will take the data of Table 4.3 and plot a position-time graph step by step on graph paper.
Steps
- On graph paper, draw the X-axis (time) and Y-axis (position) meeting at origin O.
- Choose scales: X-axis 5 divisions = 1 s; Y-axis 5 divisions = 20 m. Mark the values.
- Plot each (time, position) point from Table 4.3; at 0 s the point is the origin itself.
- Join all points — for Table 4.3 they form a straight line (Fig. 4.11c).
What you observe
- A straight-line position-time graph means equal distances in equal times — constant velocity .
- A graph is not a route map — it shows how position changes with time, not the path taken.
ā Example 4.5 — For a vehicle starting from
For a vehicle starting from rest and speeding up, the data are below. Plot the position-time graph.
| Time | 0 s | 2 s | 4 s | 6 s | 8 s | 10 s | 12 s |
|---|---|---|---|---|---|---|---|
| Position | 0 m | 1 m | 4 m | 9 m | 16 m | 25 m | 36 m |
Using scales X: 5 divisions = 2 s, Y: 5 divisions = 5 m and plotting the points, they do not fall on a straight line. Joining them gives a curve (Fig. 4.12) — the velocity is changing, so the motion is accelerated.
