ANAND CLASSES study material and notes to understand the concept of position-time graphs with detailed explanations, examples, and graph interpretations. Learn how to analyze uniform and non-uniform motion through graphs, along with exam-oriented Q&A, MCQs, worksheets, and a test paper. Perfect for JEE, NEET, and CBSE Board Class 11 students.
Introduction
The position-time graph is a fundamental concept in kinematics, representing how the position of an object changes with respect to time. It provides crucial insights into the nature of motion, helping to determine:
Whether motion is uniform or non-uniform.
The velocity of an object.
Acceleration (in the case of non-uniform motion).
A position-time graph is drawn by plotting time on the x-axis and position on the y-axis. Depending on the type of motion, the graph can be a straight line or a curve.
Position-Time Graph for a Body at Rest
Concept:
When an object remains stationary at a certain position, the position-time graph is a horizontal line parallel to the time axis.
This indicates that the object’s position does not change with time, implying zero velocity.
Example:
Consider a ball placed at a fixed position of 20 meters from the origin. Even after 5 seconds, the ball remains in the same position. The graph will be a straight horizontal line parallel to the time axis.
Graph Interpretation:
Position-Time Graph for a Body at Rest
X-axis: Time (seconds)
Y-axis: Position (meters)
Nature of Graph: Horizontal straight line
Key Observations:
A horizontal line indicates no change in position.
The object is at rest throughout the given time interval.
Position-Time Graph for Uniform Motion
Concept:
When an object moves with uniform motion, it covers equal distances in equal time intervals.
The position-time graph for uniform motion is a straight line inclined to the time axis.
The slope of this straight line represents the velocity of the object.
Example:
A car moves at a constant speed, covering 10 meters per second for 5 seconds. The position-time data is given in the table:
Time (s)
Position (m)
1
10
2
20
3
30
4
40
5
50
Graph Interpretation:
Position-Time Graph for Uniform Motion
X-axis: Time (seconds)
Y-axis: Position (meters)
Nature of Graph: Straight line inclined to the time axis
Slope of Graph: Constant, representing uniform velocity
Key Observations:
The steeper the slope, the higher the velocity.
A straight-line graph confirms constant velocity (uniform motion).
A negative slope (downward trend) would indicate motion in the opposite direction.
Position-Time Graph for Non-Uniform Motion
Concept:
In non-uniform motion, the object covers unequal distances in equal time intervals.
The position-time graph is a curve, as the velocity is not constant.
If the curve is bending upwards, it indicates acceleration (increasing velocity).
Example:
A train starts from rest, gains speed, moves with uniform velocity for some time, and then slows down before stopping at the next station.
Graph Interpretation:
Position-Time Graph for Non-Uniform Motion
X-axis: Time (seconds)
Y-axis: Position (meters)
Nature of Graph: Curved line indicating changing velocity
Key Feature: A changing slope signifies acceleration or deceleration
Key Observations:
A graph bending upwards shows increasing velocity (positive acceleration).
A graph bending downwards shows decreasing velocity (negative acceleration or deceleration).
A steeper slope at later points indicates acceleration.
Exam-Oriented Questions and Answers
Q1: How can you differentiate between uniform and non-uniform motion using a position-time graph?
Answer:
A straight-line graph inclined to the time axis represents uniform motion (constant velocity).
A curved graph represents non-uniform motion, indicating changing velocity due to acceleration or deceleration.
Q2: What does the slope of a position-time graph represent?
Answer:
The slope represents the velocity of the object.
A steeper slope means higher velocity, while a horizontal line indicates zero velocity.
MCQs with Answers and Explanations
Q1: What is the shape of a position-time graph for an object at rest?
A) Straight line inclined to the time axis B) Horizontal straight line ✅ C) Parabolic curve D) Vertical line
Explanation: Since the object is at rest, its position does not change with time, resulting in a horizontal straight-line graph.
Q2: What does a curved position-time graph indicate?
A) Constant velocity B) Changing velocity ✅ C) Object is at rest D) Object moves with uniform motion
Explanation: A curved graph represents non-uniform motion, where velocity changes with time due to acceleration or deceleration.
Do You Know? (Interesting Facts)
The steeper the slope of a position-time graph, the higher the velocity of the object.
If two objects have the same position-time graph, they have the same velocity.
A parabolic position-time graph represents uniformly accelerated motion, such as free fall.
Worksheet
Solve the following questions:
A car moves 5m every second for 10 seconds. Draw its position-time graph.
If a body is at rest at 30m from the origin, sketch the position-time graph.
Describe the motion represented by a straight line passing through the origin in a position-time graph.
Test Paper (10 Marks)
Question
Marks
Define position-time graph and its significance.
2
Draw a position-time graph for a uniformly moving object.
2
Explain how the slope of a position-time graph represents velocity.
2
Differentiate between uniform and non-uniform motion.
2
Give an example where a position-time graph is a curve.
2
Important Points for Quick Revision
Horizontal line → Object at rest
Inclined straight line → Uniform motion
Curved line → Non-uniform motion
Slope of the graph = Velocity of the object
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