Graphical Representation of Motion

Discover how graphs help us visualize and understand motion! Learn to interpret distance-time and velocity-time graphs, and understand what they tell us about an object's motion.

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Why Use Graphs?
Graphs provide a convenient method to present information about motion. Just like bar graphs show cricket run rates, line graphs help us understand how distance and velocity change with time.
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Motion Graphs
Line graphs show the dependence of one physical quantity (like distance or velocity) on another quantity (like time). This helps us analyze and predict motion patterns.
Uniform Motion
Distance ∝ Time (Straight line)
When an object moves with uniform speed, it travels equal distances in equal time intervals. The graph is a straight line showing direct proportionality.
Non-Uniform Motion
Distance ∝ Time² (Curved line)
When an object moves with changing speed (acceleration), the distance-time graph is curved, showing non-linear variation.
Uniform Velocity
Constant velocity = Horizontal line parallel to time axis
Uniform Acceleration
Constant acceleration = Straight line with constant slope
Non-Uniform Acceleration
Variable acceleration = Curved line with changing slope
Area Under Velocity-Time Graph
Area = Distance Travelled
  • The area enclosed by velocity-time graph and time axis equals displacement
  • For uniform velocity: Area = Rectangle = v × t
  • For uniform acceleration: Area = Rectangle + Triangle
  • Area = (u × t) + ½ × (v - u) × t
  • This gives us the total distance travelled
s = ut + ½at²
Interactive Area Calculation
Click on the graph to see area calculation

NCERT Data Tables

Table 7.2: Car Distance Data
Time (s) Distance (m)
00
21
44
69
816
1025
1236
Table 7.3: Car Velocity Data
Time (s) Velocity (m/s) Velocity (km/h)
000
52.59
105.018
157.527
2010.036
2512.545
3015.054
Create Your Graph
Generate a graph to see calculations
Interactive Graph

NCERT Activities

Activity 7.9: Train Journey
Table 7.4: Train Schedule
Station A (0 km): Departure 08:15
Station B (120 km): Arrival 11:15, Departure 11:30
Station C (180 km): Arrival 13:00

Plot and interpret the distance-time graph for the train.
Activity 7.10: Feroz and Sania's Bicycle Race
Table 7.5: Distance covered by both students
Compare their motion patterns and determine who reaches school first. Both follow the same route but take different times.

Practice Questions

Q1.
What is the nature of the distance-time graphs for uniform and non-uniform motion of an object?
Answer:
Uniform motion: The distance-time graph is a straight line passing through the origin, showing that distance is directly proportional to time.

Non-uniform motion: The distance-time graph is a curved line (parabola for uniformly accelerated motion), showing non-linear variation of distance with time.
Q2.
What can you say about the motion of an object whose distance-time graph is a straight line parallel to the time axis?
Answer: If the distance-time graph is a straight line parallel to the time axis, it means the object is at rest. The distance remains constant with time, indicating zero velocity and no motion.
Q3.
What can you say about the motion of an object if its speed-time graph is a straight line parallel to the time axis?
Answer: If the speed-time (or velocity-time) graph is a straight line parallel to the time axis, it means the object is moving with uniform velocity. The speed remains constant, so acceleration is zero.
Q4.
What is the quantity which is measured by the area occupied below the velocity-time graph?
Answer: The area under the velocity-time graph represents the displacement (or distance travelled) by the object. For uniform velocity, Area = velocity × time. For accelerated motion, the area includes both rectangular and triangular portions.
Explore Motion Graphs
Understanding Motion Graphs
Graphs provide a visual representation of motion that helps us understand relationships between physical quantities. Line graphs show how one quantity depends on another, making complex motion patterns easy to analyze and interpret.
Distance-Time Graphs
• Uniform motion: Straight line (distance ∝ time)
• Non-uniform motion: Curved line
• At rest: Horizontal line
• Slope: Represents speed
Velocity-Time Graphs
• Uniform velocity: Horizontal line
• Uniform acceleration: Straight inclined line
• Non-uniform acceleration: Curved line
• Area under curve: Displacement
Speed = Slope of Distance-Time Graph
Acceleration = Slope of Velocity-Time Graph
Displacement = Area under Velocity-Time Graph
Key Points to Remember
• Graphs make motion analysis visual and intuitive
• Slope of distance-time graph gives speed
• Slope of velocity-time graph gives acceleration
• Area under velocity-time graph gives displacement
• Straight lines indicate uniform motion
• Curved lines indicate non-uniform motion
• Horizontal lines indicate constant values