You are here
What does the shape of a position-time graph tell us — and can we pull velocity out of it?
- A straight line means equal displacements in equal times — constant velocity .
- A curved line means the velocity is not constant — the object is accelerating .
- A line parallel to the time axis means the position is not changing — the object is at rest .
- Take a part AB of the line. Drawing lines parallel to the axes forms a triangle ABC where BC = change in position \((s_2 - s_1)\) and AC = change in time \((t_2 - t_1)\).
- The slope \(\dfrac{BC}{CA} = \dfrac{s_2 - s_1}{t_2 - t_1}\) gives the average velocity. For example: $$v = \dfrac{80 - 40}{4 - 2} = \dfrac{40}{2} = 20\ \text{m s}^{-1}$$
- The slope of a graph shows the rate of change of the Y-quantity with respect to the X-quantity.
- Position-time graph — a graph that represents the motion of an object, i.e. the change in its position with time.
- Slope — the steepness of a line; the slope of a graph gives the rate of change of the Y-quantity with respect to the X-quantity (here, the velocity).
- For a curved position-time graph too, the velocity at any instant can be found geometrically from the graph. You will learn how to do this in higher grades.
In this Activity, we will calculate the average velocity from a position-time graph by forming a triangle on the line and finding its slope.
- On the graph of Fig. 4.11c, pick a part AB. From A draw lines parallel to the X- and Y-axes; repeat from B to form triangle ABC.
- BC represents \((s_2 - s_1)\) and CA represents \((t_2 - t_1)\).
- Average velocity \(= \dfrac{BC}{CA}\). Reading values: \(\dfrac{80\text{ m} - 40\text{ m}}{4\text{ s} - 2\text{ s}} = 20\ \text{m s}^{-1}\).
- The slope of the position-time line equals the average velocity over that interval.
What does a horizontal position-time line at 40 m (Fig. 4.15) tell us?
The position stays 40 m and does not change with time, so the object is at rest at 40 m from the origin. A line parallel to the time axis on a position-time graph represents a stationary object.
Two objects A and B have straight position-time lines (Fig. 4.16). Whose average velocity is higher?
For the same time interval, B’s displacement is larger, so the line for B is steeper (greater slope). A steeper slope means greater velocity, so B has the higher velocity .
NCERT Question 6 — Fig. 4.27 shows a position-time
Two objects A and B move on parallel tracks in the same direction (Fig. 4.27). Do they ever have equal velocity?
View the answer →NCERT Question 7 — A graph in Fig. 4.28
A and B have the same start and end positions over 0–10 s (Fig. 4.28). Choose the correct option(s) on their average velocity and speed.
View the answer →