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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 BC CA = s 2 - s 1 t 2 - t 1 gives the average velocity. For example: v = 80 - 40 4 - 2 = 40 2 = 20 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 = BC CA . Reading values: 80 m - 40 m 4 s - 2 s = 20 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
Fig. 4.27 shows a position-time graph of two objects A and B that are moving along the parallel tracks in the same direction. Do objects A and B ever have equal velocity? Justify your answer.
NCERT Question 7 — A graph in Fig. 4.28
A graph in Fig. 4.28 shows the change in position with time for two objects A and B moving in a straight line from 0 to 10 seconds. Choose the correct option(s).
(i) The average velocity of both over the 10 s time interval is equal since they have the same initial and final positions.
(ii) The average speeds of both over the 10 s time interval are equal since both cover equal distance in equal time.
(iii) The average speed of A over the 10 s time interval is lower than that of B since it covers a shorter distance than B in 10 seconds.
(iv) The average speed of A over the 10 s time interval is greater than that of B since B’s speed is lower than A’s in some segments.
