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Assertion-Reason type. Each of these contains two Statements: Statement I (Assertion), Statement II (Reason). Each of these questions also has four alternative choice, only one of which is correct. You have to select the correct choices from the codes (a), (b), (c) and (d) given below (a) If both Assertion and Reason are true and the Reason is correct explanation of the Assertion (b) If both Assertion and Reason are true but Reason is not correct explanation of the Assertion (c) If Assertion is true but Reason is false (d) If Assertion is false but the Reason is true Assertion The slope of displacement-time graph of a body movng with high velocity is steeper than the slope of displacement-time graph of a body with low velocity. Reason Slope of displacement-time graph = Velocity of the body.

Step by step solution

01

Understand the Assertion

The Assertion states that the slope of the displacement-time graph of a body moving with high velocity is steeper than the slope of such a graph for a body with low velocity. A steeper slope indicates a larger value of the slope.

02

Understand the Reason

The Reason states that the slope of a displacement-time graph is equal to the velocity of the body. This means that if a body has a higher velocity, the graph's slope will be greater.

03

Evaluate the Truth of Assertion and Reason

Both Statement I (Assertion) and Statement II (Reason) are true. A steeper slope does correspond to a higher velocity because the slope of a displacement-time graph represents velocity.

04

Determine the Correct Explanation

The Reason correctly explains the Assertion because the slope of the displacement-time graph directly represents velocity. Thus, a higher velocity implies a steeper slope.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Displacement-Time Graph

Understanding a displacement-time graph is key in analyzing the motion of an object over time. This graph plots time on the horizontal axis and displacement on the vertical axis. Here's what you need to know:

• Displacement: It's the change in position of an object, measured as the shortest path between the starting point and the end point. It's a vector quantity, meaning it has both magnitude and direction.
• Time: This is always placed on the x-axis, allowing you to track changes in displacement over specific time intervals.
• Slope Interpretation: Each point on the graph represents the displacement of the object at a specific time. The line connecting these points helps you determine how displacement changes with time, giving valuable insights into the object's motion.

A straight line indicates uniform motion, while a curved line suggests acceleration. The graph's slope at any point gives the object's velocity, which leads us to discuss velocity further.

Velocity

When talking about the motion of an object, velocity is a fundamental concept. It gives us a clear indication of how fast an object is moving and in which direction. Velocity is often confused with speed, but they differ:

• Velocity vs Speed: Both terms describe motion, but velocity includes direction, while speed is a scalar quantity indicating how fast the object is moving regardless of its direction.
• Calculating Velocity: On a displacement-time graph, velocity is represented by the slope. If the graph is linear, the motion is at a constant velocity. If the graph is curved, the instantaneous velocity can be found by drawing a tangent to the curve at any point.
• High and Low Velocities: A steep slope suggests high velocity, meaning the object covers more distance in less time. A shallow slope points to a lower velocity.

By understanding these facets of velocity, you can better interpret displacement-time graphs and the motion they represent.

Slope Analysis

The slope of a displacement-time graph is more than just a line; it's a powerful tool for understanding motion. It signifies the velocity of the object. Here's how you can make the most of slope analysis:

• Calculating Slope: Slope in such a graph is calculated by the formula \( \text{Slope} = \frac{\Delta y}{\Delta x} \) where \( \Delta y \) is the change in displacement and \( \Delta x \) is the change in time.
• Interpreting Slope Values: A greater slope value signifies higher velocity. Thus, different slopes on the displacement-time graph can indicate when an object is speeding up, slowing down, or moving at a constant speed.
• Applications of Slope Analysis: This analysis allows you to predict future motion, determine past conditions, or compare different object movements at a glance.

Using slope analysis is essential not only in physics but also in various practical applications. It helps to visually grasp the concept of velocity and acceleration in everyday life scenarios.