Position-Time Graph for uniform and non-uniform motion, MCQs, Q&A, Worksheet, Question Paper

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:

• 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:

Graph Interpretation:

• 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:

• 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:

1. A car moves 5m every second for 10 seconds. Draw its position-time graph.
2. If a body is at rest at 30m from the origin, sketch the position-time graph.
3. Describe the motion represented by a straight line passing through the origin in a position-time graph.

Test Paper (10 Marks)

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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