Describing Motion Around Us · Lesson 6 of 10
Position-time graphs
“A sloping line quietly tells you how fast position is changing.”
• Read position from a position-time graph. • Identify constant and changing velocity from graph shape. • Recognise a stationary object from a horizontal line. • Calculate average velocity from graph coordinates. • Interpret slope as rate of change of position. • Compare velocities using graph steepness.
Imagine watching only a graph while a vehicle moves behind a wall. A rising straight line, a curve and a horizontal line would tell three different stories. The graph’s height gives position, while the way that height changes gives velocity.
A position-time graph shows how an object’s position changes with time.
A straight sloping line shows that equal position changes occur in equal time intervals, so velocity is constant. A curved line shows that the position changes by unequal amounts in equal intervals, so velocity changes. A horizontal line shows that the position remains fixed, so the object is at rest relative to the origin.
Activity: Let us calculate
Choose two points (A(t_1,s_1)) and (B(t_2,s_2)) on a straight position-time graph. Draw horizontal and vertical guide lines to form a right triangle. The vertical side represents (s_2-s_1), while the horizontal side represents (t_2-t_1). Their ratio is the average velocity.
The slope of a graph is the change in the vertical-axis quantity divided by the corresponding change in the horizontal-axis quantity.
Problem
A straight graph passes through 40 m at 2 s and 80 m at 4 s. Find velocity.
- 1.Write the two points: (A(2 s,40 m)) and (B(4 s,80 m)).
- 2.Change in position = (80-40=40 m).
- 3.Change in time = (4-2=2 s).
- 4.Velocity = (40÷2=20 m s⁻¹).
- 5.Because the graph is straight, the same slope applies throughout the shown motion.
Problem
A graph remains at 40 m from 0 s to 3 s. What does it show?
- 1.At every shown time, the position is 40 m.
- 2.Change in position is zero.
- 3.Slope = (0÷3=0 m s⁻¹).
- 4.The object is stationary 40 m from the origin.
- 5.The graph is not a distance-time graph because the object is not covering additional distance.
Problem
Two straight position-time graphs cover the same time interval, but line B is steeper than line A. Which object has greater velocity magnitude?
- 1.Slope represents velocity.
- 2.Both lines use the same axes and time scale.
- 3.The steeper line has a larger change in position for the same time.
- 4.Therefore, object B has the greater velocity magnitude.
Ready to Go Beyond
For a curved position-time graph, the average velocity between two points comes from the slope of the joining line. Velocity at one instant is associated with the slope of the tangent to the curve at that instant. The detailed tangent method is developed later; the essential idea is that local steepness represents how quickly position is changing.
A horizontal position-time line means zero velocity. Its height may represent any fixed position, including a non-zero one.
Quiz
Which description best matches Position-Time Graph?
Which description best matches Slope?
Which term matches this description: A position-time graph shows how an object’s position changes with time.
Which term matches this description: The slope of a graph is the change in the vertical-axis quantity divided by the corresponding change in the horizontal-axis quantity.
Which statement is a key takeaway from this lesson?
Practice Problems
- A graph changes from 10 m at 2 s to 70 m at 5 s. Find average velocity.
- Describe the graph of an object at rest 25 m from the origin.
- Two lines have slopes 4 m s⁻¹ and 7 m s⁻¹. Compare their motions.
- Explain why a curved position-time graph represents changing velocity.
Key Takeaways
• Graph height gives position. • A straight sloping line shows constant velocity. • A curve shows changing velocity. • A horizontal line shows rest. • Slope of a position-time graph gives velocity.