The velocity-time graph for a body with non-uniform motion is a :

A. straight line

B. straight line parallel to the X-axis

C. straight line parallel to the Y-axis

D. curved line

When we talk about the velocity-time graph for a body in non-uniform motion, the correct answer is D: curved line. Let’s break down why that is the case and what it means in the context of motion.

Understanding Non-Uniform Motion

Non-uniform motion refers to a situation where the velocity of an object changes over time. This can happen due to various factors, such as acceleration or deceleration. Unlike uniform motion, where the velocity remains constant, non-uniform motion involves variations in speed and direction.

Velocity-Time Graph Basics

A velocity-time graph plots velocity on the vertical axis (Y-axis) and time on the horizontal axis (X-axis). The shape of the graph provides insights into the motion of the object:

• Straight Line: Indicates constant velocity (uniform motion).
• Horizontal Line: Shows that the object is at rest (velocity = 0).
• Vertical Line: Not applicable in this context, as it would imply an infinite change in velocity over no time, which is physically impossible.
• Curved Line: Represents changing velocity, indicating acceleration or deceleration.

Why a Curved Line for Non-Uniform Motion?

In non-uniform motion, the velocity of the object is not constant; it changes over time. This change can be gradual or abrupt, leading to a graph that curves. For example, if an object is accelerating, the velocity increases, and the graph will curve upwards. Conversely, if the object is decelerating, the graph will curve downwards.

Examples to Illustrate

Consider a car that starts from rest and gradually speeds up. Initially, the velocity increases slowly, then more rapidly as the car accelerates. If you were to plot this on a velocity-time graph, you would see a curve that starts at the origin and rises steeply as time progresses.

On the other hand, if the car were to apply brakes, the velocity would decrease, and the graph would curve downwards. This illustrates how the shape of the graph reflects the nature of the motion.

Visualizing the Concept

Imagine a roller coaster. As it climbs to the top, it slows down, and the velocity decreases. As it descends, the velocity increases rapidly. If you were to graph the velocity of the roller coaster over time, you would see a curve that reflects these changes in speed.

In summary, the velocity-time graph for a body in non-uniform motion is indeed a curved line, as it effectively captures the variations in velocity over time. Understanding this concept is crucial for analyzing motion in physics, as it helps us visualize and interpret how objects move in the real world.