How to Find Speed from a Distance-Time Graph with Solved Questions
A distance-time graph visually shows how far an object travels over time in a straight line. On these graphs, distance is plotted on the vertical axis (Y-axis) and time on the horizontal axis (X-axis). Interpreting the shape and slope of a distance-time graph helps you understand both the speed and motion pattern of an object—whether it moves at a steady speed, accelerates, slows down, or stays still.
Understanding Distance-Time Graphs
If distance increases at a steady rate as time passes, the line is straight and sloped upwards. The steeper the line, the greater the speed. If the line flattens (runs horizontally), the object is stationary. Curved lines mean the speed is changing: if the curve gets steeper, the object accelerates; if it becomes less steep, the object slows down.
Distance-time graphs allow you to calculate speed by measuring the gradient (slope) between any two points. A higher gradient means faster movement.
| Section of Graph | Gradient | Speed | Physical Meaning |
|---|---|---|---|
| A (Curve gets steeper) | Increasing | Increasing | Object is accelerating (speeding up) |
| B (Straight line, constant slope) | Constant | Constant | Object moves with steady speed |
| C (Curve becomes less steep) | Decreasing | Decreasing | Object is decelerating (slowing down) |
| D (Horizontal line) | Zero | Zero | Object is stationary (at rest) |
Key Formulas for Distance-Time Graphs
| Concept | Formula | How to Use |
|---|---|---|
| Speed (for straight lines) | Speed = Distance / Time | Use total distance and total time between two points |
| Gradient (for straight lines) | Gradient = Change in Distance ÷ Change in Time | Pick two points: (t₁, d₁) to (t₂, d₂) Calculate (d₂–d₁)/(t₂–t₁) |
| Speed at a point (on a curve) | Gradient of tangent at that point | Draw a tangent; find its slope as above |
Worked Examples
Example 1: Calculate the speed for an object whose distance increases from 0 m to 8 m in 4 s.
Solution:
Change in distance = 8 m – 0 m = 8 m
Change in time = 4 s – 0 s = 4 s
Speed = 8 m ÷ 4 s = 2 m/s
Example 2: On another straight section, the distance goes from 0 m to 10 m in 2 s. Find the speed.
Solution:
Change in distance = 10 m
Change in time = 2 s
Speed = 10 m ÷ 2 s = 5 m/s
How to Approach Problem Solving with Distance-Time Graphs
- Identify the axes: X should be time, Y should be distance. Check the units.
- Look at the graph’s shape:
– Upward straight line: constant speed
– Horizontal segment: no movement
– Curved line: changing speed (acceleration or deceleration) - To find speed for straight segments, use the speed formula or find the gradient.
- For curves (changing speed), draw a tangent at the point of interest and measure its gradient for instantaneous speed.
- Always state the time interval and label it clearly.
When Does Acceleration Appear in Distance-Time Graphs?
Acceleration or deceleration is represented by a curve. If the slope (gradient) of the curve increases, the object accelerates. If the slope decreases, it decelerates. You may measure the gradient at specific points by drawing tangents for such cases.
Remember, constant speed is a straight (diagonal) line, while acceleration creates a curve.
Further Learning and Practice
Mastering how to read and apply distance-time graphs forms a foundation for many topics: speed-time graphs, motion in a straight line, and uniform or accelerated motion. Explore these Vedantu topics for deeper insight:
- Distance-Time Graph for Uniform Velocity
- Speed-Time Graphs
- Velocity-Time Graphs
- Motion in a Straight Line
- Kinematics Equations
- Uniform and Non-uniform Motion
Summary
A distance-time graph is a core Physics tool for describing and analysing motion. The graph’s slope always represents speed – the steeper the line, the faster the object is moving. Understanding the motion’s nature (constant, accelerating, stationary) is a matter of reading line shapes and calculating gradients.
Regular practice with different scenarios builds confidence and prepares you for higher-level Physics challenges. Explore further with the linked Vedantu resources for structured topic-by-topic study and problem-solving.
FAQs on Distance–Time Graph: Meaning, Interpretation & Examples
1. What is a distance-time graph?
A distance-time graph is a visual representation of how the distance traveled by an object changes with time.
- The X-axis shows time, and the Y-axis shows distance from a fixed point.
- It helps describe motion (uniform or non-uniform), rest, and speed.
2. What does the slope of a distance-time graph represent?
The slope of a distance-time graph indicates the speed of the object.
- Formula: Slope = Change in Distance / Change in Time
- A steeper slope means a higher speed.
- If the line is horizontal, speed is zero (object at rest).
3. How do you draw a distance-time graph for uniform motion?
For uniform motion, the distance-time graph is a straight line with a constant positive slope.
- Plot time on the X-axis and distance on the Y-axis.
- Mark points where distance increases equally with time.
- Connect the points to get a straight line passing through the origin if starting from rest.
4. What does a horizontal line on a distance-time graph indicate?
A horizontal line on a distance-time graph means the object is at rest.
- Distance does not change with time, so speed is zero.
5. How can you tell if the motion is non-uniform from a distance-time graph?
If the distance-time graph is a curved line, it shows non-uniform motion.
- The slope (speed) keeps changing, indicating acceleration or deceleration.
- A curve getting steeper means increasing speed (acceleration).
- A curve getting flatter means decreasing speed (deceleration).
6. How is speed calculated from a distance-time graph?
Speed is calculated as the slope of the distance-time graph.
- Pick two points: (t1, d1) and (t2, d2).
- Speed = (d2 – d1) / (t2 – t1).
7. What information can you NOT determine from a distance-time graph?
You cannot determine direction or negative values from a simple distance-time graph.
- It only shows the magnitude of distance, not direction or displacement.
- To study direction, use a displacement-time or velocity-time graph.
8. What is the difference between distance-time and velocity-time graphs?
A distance-time graph shows how distance changes over time, while a velocity-time graph shows how speed or velocity changes over time.
- Distance-time: Slope gives speed; area under curve has no meaning.
- Velocity-time: Slope gives acceleration; area under the curve gives displacement.
9. Can the distance-time graph show objects moving backward?
No, a standard distance-time graph cannot show backward (negative) motion, as distance cannot decrease; it is always positive or zero.
- If the graph goes flat, it means the object is at rest, not moving backward.
10. Why is mastering distance-time graphs important for exams?
Distance-time graphs are frequently tested in board and entrance exams because they assess graph reading, interpretation, and problem-solving skills.
- Questions can ask you to draw, interpret, or calculate from these graphs.
- They build a foundation for advanced Physics concepts like kinematics and motion analysis.
11. What are common mistakes students make with distance-time graphs?
Common mistakes include confusing the X and Y axes, misinterpreting a curve as uniform motion, and calculating slope incorrectly.
- Always label axes clearly.
- Check if the line is straight or curved before finding speed.
- Use correct units for all answers.
12. How can I practice distance-time graph problems effectively?
Practice by solving sample graphs, MCQs, and previous year's questions with detailed solutions.
- Download worksheets and attempt step-wise problems.
- Analyze Vedantu’s solved examples to understand exam patterns.
- Review common question types and practice graphical interpretation.
