Interactive physics simulator
Distance-Time Graph
A distance-time graph shows how the distance traveled by an object changes with time. The slope of the graph tells the speed of the object.
Distance-Time Graph Simulator
Watch the object move and the graph draw at the same time. The graph slope is the speed.
Live Result
- Initial distance
- 0 m
- Current distance
- 0 m
- Timer
- 0 s
- Total time
- 6 s
- Speed
- 2 m/s
- Graph slope
- 2 m/s
- Graph point
- (0 s, 0 m)
- Unit
- m/s
- Formula
- slope = Δd / Δt
What is a Distance-Time Graph?
A distance-time graph is not a picture of the actual path. It is a graph that compares distance traveled with time. Time goes on the horizontal axis, distance goes on the vertical axis, and the slope tells speed.
Key Definition
A distance-time graph shows how distance traveled changes with time.
- Time is shown on the horizontal x-axis.
- Distance is shown on the vertical y-axis.
- The slope of the graph shows speed.
- A steeper line means greater speed.
- A horizontal line means the object is at rest.
- Distance cannot be negative in a distance-time graph.
Distance-Time Graph Formula
Speed = Distance / Time
Speed = Slope = Change in Distance / Change in Time
slope = Δd / Δt
d is distance, t is time, Δd is change in distance, and Δt is change in time.
Use meters for distance, seconds for time, and m/s for speed.
What Different Lines Mean
Steep straight line
Object is moving fast. Greater slope means greater speed.
Gentle straight line
Object is moving slowly. Smaller slope means smaller speed.
Horizontal line
Object is at rest. Distance is not changing, so speed is zero.
Curved line
Speed is changing. This means non-uniform motion.
Real-life Example of a Distance-Time Graph
A ball moves at a constant speed of 2 m/s for 5 seconds.
Time = 5 s, Speed = 2 m/s, so Distance = 2 x 5 = 10 m.
- A drone hovering in one place creates a horizontal distance-time graph.
- A train capsule moving faster creates a steeper graph line.
Solved Examples
A graph shows distance increasing from 0 m to 20 m in 5 s. Find speed.
- Speed = Change in Distance / Change in Time
- Speed = 20 / 5
- Speed = 4 m/s
Answer: 4 m/s
A graph is horizontal at 10 m from 0 s to 6 s. What is the speed?
- Distance does not change.
- Change in distance = 0 m.
- Speed = 0 m/s, so the object is at rest.
Answer: 0 m/s
A graph rises from 5 m at 2 s to 25 m at 6 s. Find speed.
- Change in distance = 25 - 5 = 20 m
- Change in time = 6 - 2 = 4 s
- Speed = 20 / 4 = 5 m/s
Answer: 5 m/s
Common Mistakes
- Thinking the graph is a picture of the actual path.
- Forgetting time is always on the x-axis.
- Forgetting distance is on the y-axis.
- Thinking a horizontal line means the object is moving horizontally.
- Forgetting horizontal line means rest.
- Confusing steepness with distance instead of speed.
- Using total distance instead of change in distance for a segment.
- Confusing distance-time graph with velocity-time graph.
Quick Summary
- Distance-time graph shows distance against time.
- x-axis shows time.
- y-axis shows distance.
- Slope shows speed.
- Steeper line means faster motion.
- Horizontal line means rest.
- Straight sloped line means uniform motion.
- Curved line means changing speed.
Practice Questions
1. A graph rises from 0 m to 30 m in 10 s. Find speed.
Speed = 30 / 10 = 3 m/s.
2. A graph is horizontal from 2 s to 8 s. What does it mean?
Distance is not changing, so the object is at rest and speed is 0 m/s.
3. Which graph line means faster speed: steep or gentle?
A steeper line means faster speed.
4. What quantity is shown on the x-axis of a distance-time graph?
Time is shown on the x-axis.
5. What quantity is shown on the y-axis of a distance-time graph?
Distance is shown on the y-axis.
6. What does the slope of a distance-time graph represent?
The slope represents speed.
FAQ
Frequently Asked Questions
What is a distance-time graph?
A distance-time graph shows how the distance traveled by an object changes with time.
What is shown on the x-axis of a distance-time graph?
Time is shown on the x-axis, usually in seconds.
What is shown on the y-axis of a distance-time graph?
Distance is shown on the y-axis, usually in meters.
What does the slope of a distance-time graph represent?
The slope of a distance-time graph represents speed.
What does a steeper distance-time graph mean?
A steeper line means the object is moving faster.
What does a horizontal line mean on a distance-time graph?
A horizontal line means distance is not changing, so the object is at rest.
What does a straight sloped line mean?
A straight sloped line means the object is moving with constant speed, also called uniform motion.
What does a curved distance-time graph mean?
A curved distance-time graph means the speed is changing, so the motion is non-uniform.
Can distance be negative on a distance-time graph?
No. Distance cannot be negative because it represents total path length traveled.
How does the distance-time graph simulator work?
The simulator moves an object and draws the distance-time graph live. It calculates speed from the slope of the graph.