Which one of the following statements is not correct?

1. Basics of Motion: Position, Displacement, and Velocity (basic)

To understand how the physical world works, we must first master the language used to describe an object's location and its movement. Position is the most fundamental of these concepts; it is the location of an object relative to a specific reference point, often called the origin. When an object changes its position over time, we say it is in motion. In its simplest form, motion occurs along a straight line, which we call linear motion Science-Class VII . NCERT(Revised ed 2025), Measurement of Time and Motion, p.116.

Crucially, we must distinguish between the path taken and the change in position. Distance is the total path length traveled by an object; it is a scalar quantity, meaning it only has a magnitude (a size). Displacement, however, is a vector quantity; it represents the shortest straight-line distance between the initial and final positions, including the direction. For example, if a train travels from Station A to Station B and then returns immediately to Station A, its total distance is the sum of both trips, but its displacement is zero because its final position is identical to its starting position.

Feature	Distance	Displacement
Definition	Total path length covered.	Shortest path between start and end.
Type	Scalar (Magnitude only).	Vector (Magnitude and Direction).
Value	Always positive or zero.	Can be positive, negative, or zero.

Once we understand displacement, we can define Velocity. Velocity is the rate of change of displacement over time (Velocity = Displacement / Time). Unlike speed, which only tells us how fast an object is going, velocity tells us how fast and in what direction it is moving. When an object moves at a constant speed in a single direction, covering equal distances in equal time intervals, it is in uniform linear motion Science-Class VII . NCERT(Revised ed 2025), Measurement of Time and Motion, p.117. If the speed or the direction changes, the motion becomes non-uniform.

Sources: Science-Class VII . NCERT(Revised ed 2025), Measurement of Time and Motion, p.116; Science-Class VII . NCERT(Revised ed 2025), Measurement of Time and Motion, p.117

2. Understanding Acceleration and Retardation (basic)

Concept: Understanding Acceleration and Retardation

3. Newton’s Second Law: Link between Force and Acceleration (intermediate)

In our previous hops, we explored how objects move (kinematics); now, we look at why they move. Newton’s Second Law is the bridge between the 'cause' (Force) and the 'effect' (Acceleration). A force is essentially a push or a pull resulting from an interaction between objects Science, Class VIII. NCERT, Exploring Forces, p.77. While we often think of force as something that moves an object, it is more accurately described as the agent that changes an object's state of motion—either its speed, its direction, or both.

The mathematical heart of this law is the famous equation F = ma (Force = mass × acceleration). This tells us that the acceleration of an object depends on two variables: the net force acting upon the object and the mass of the object. The SI unit of force is the newton (N) Science, Class VIII. NCERT, Exploring Forces, p.65. It is crucial to understand that acceleration is the rate of change of velocity. If an object is moving at a constant speed in a straight line (uniform linear motion), the net force acting on it is zero because its velocity isn't changing Science, Class VII. NCERT, Measurement of Time and Motion, p.118.

One of the most common pitfalls for students is the relationship between instantaneous velocity and acceleration. Does zero velocity mean zero acceleration? Not necessarily. Imagine throwing a ball straight up into the air. At the very peak of its flight, the ball stops for a tiny fraction of a second—its instantaneous velocity is zero. However, gravity is still pulling it down with a constant acceleration of approximately 9.8 m/s². If the acceleration were also zero at that peak, the ball would simply hang in the air forever! This demonstrates that acceleration depends on the force being applied, not the current speed of the object.

Scenario	Velocity (v)	Acceleration (a)	Resulting Motion
Force in direction of motion	Positive	Positive	Object speeds up
Force opposite to motion	Positive	Negative	Object slows down (deceleration)
Peak of a vertical throw	Zero	Non-Zero (Gravity)	Object changes direction

Sources: Science, Class VIII. NCERT, Exploring Forces, p.77; Science, Class VIII. NCERT, Exploring Forces, p.65; Science, Class VII. NCERT, Measurement of Time and Motion, p.118

4. Motion Under Gravity: The Peak Point Paradox (intermediate)

To understand motion under gravity, we must first distinguish between velocity (how fast and in what direction something moves) and acceleration (the rate at which that velocity changes). On Earth, gravity acts as a constant downward pull, providing a near-uniform acceleration of approximately 9.8 m/s² Physical Geography by PMF IAS, The Solar System, p.23. This force is the 'universal switch' that drives the movement of all surface materials, from falling rain to the erosion of mountains FUNDAMENTALS OF PHYSICAL GEOGRAPHY, Geomorphic Processes, p.38. Even though gravity varies slightly—being stronger at the poles than at the equator due to the Earth's shape—it never simply 'turns off' while an object is in flight FUNDAMENTALS OF PHYSICAL GEOGRAPHY, The Origin and Evolution of the Earth, p.19.

The Peak Point Paradox arises when we observe an object thrown straight up into the air. As the object rises, its velocity is directed upward, but gravity pulls it downward. Because the velocity and acceleration have opposite signs, the object slows down. At the very highest point of its trajectory—the peak—the object comes to a momentary standstill. Its instantaneous velocity is zero. However, the paradox is that its acceleration is not zero. If acceleration were zero at the peak, the object would have no reason to change its state of rest and would simply hover in mid-air!

In reality, the constant acceleration of gravity (9.8 m/s²) continues to act on the object even at the peak. This persistent acceleration is what causes the velocity to change from zero to a downward direction, bringing the object back to Earth. This illustrates a fundamental rule in mechanics: an object can have zero velocity while simultaneously experiencing non-zero acceleration. We see this same principle in ocean waves, where gravity constantly pulls the crests downward to move the water body, regardless of the water's momentary vertical speed FUNDAMENTALS OF PHYSICAL GEOGRAPHY, Movements of Ocean Water, p.108.

Sources: Physical Geography by PMF IAS, The Solar System, p.23; FUNDAMENTALS OF PHYSICAL GEOGRAPHY, Geomorphic Processes, p.38; FUNDAMENTALS OF PHYSICAL GEOGRAPHY, The Origin and Evolution of the Earth, p.19; FUNDAMENTALS OF PHYSICAL GEOGRAPHY, Movements of Ocean Water, p.108

5. Graphical Interpretation of Kinematics (intermediate)

In kinematics, graphs are more than just pictures; they are visual representations of the rate of change. To understand motion, we focus on the relationship between position (x), velocity (v), and acceleration (a). From a mathematical perspective, if we have a linear relation such as y = a + bx, the constant 'b' represents the slope or the tangent of the angle of the line Macroeconomics, Determination of Income and Employment, p.58. In a position-time graph, this slope represents velocity. If the graph is upward sloping, the function is increasing; if downward, it is decreasing Microeconomics, Theory of Consumer Behaviour, p.22. Similarly, on a velocity-time graph, the slope represents acceleration.

A common point of confusion is what happens when an object momentarily stops. It is a fundamental principle that an object can have zero instantaneous velocity while still possessing a non-zero acceleration. Imagine throwing a ball straight up: at its highest point, it stops for a split second (v = 0), yet gravity continues to pull it down with a constant acceleration of 9.8 m/s². If the acceleration were also zero at that peak, the ball would simply hang in the air forever! Acceleration only becomes zero if the velocity remains zero for a finite interval of time, indicating the object is truly at rest.

Finally, the signs (positive or negative) of these variables tell us about the direction of motion. If an object has a positive position (it is to the right of the origin) but a negative velocity, it is moving back toward the origin. When velocity and acceleration have opposite signs, the acceleration is acting as a 'brake,' causing the object to slow down. Conversely, uniform linear motion occurs only when an object covers equal distances in equal intervals of time, resulting in a constant velocity and zero acceleration Science-Class VII, Measurement of Time and Motion, p.117.

Sources: Macroeconomics, Determination of Income and Employment, p.58; Microeconomics, Theory of Consumer Behaviour, p.22; Science-Class VII, Measurement of Time and Motion, p.117

6. Vector Signs: Speeding Up vs. Slowing Down (exam-level)

In the study of linear motion, we often describe how objects speed up, move at a constant pace, or slow down to a halt Science-Class VII . NCERT(Revised ed 2025), Measurement of Time and Motion, p.116. To master this for the exam, you must move beyond the everyday idea of "acceleration" and look at the mathematical signs of velocity (v) and acceleration (a).

The secret to knowing whether an object is speeding up or slowing down lies in the interaction between these two vectors:

• Speeding Up: This occurs when velocity and acceleration have the same sign. If both are positive, the object is moving forward and being pushed forward. If both are negative, the object is moving backward and being pushed even faster in that backward direction.
• Slowing Down: This occurs when velocity and acceleration have opposite signs. If you are moving forward (+v) but acceleration is acting backward (-a), it acts as a brake.

A critical nuance to remember is the Instantaneous Zero. It is a common misconception that if an object isn't moving (v = 0), it cannot be accelerating. Consider a ball thrown straight up: at the very peak of its flight, its velocity is momentarily zero. However, acceleration due to gravity is still acting on it. If acceleration were zero at that moment, the ball would simply hover in mid-air forever! Similarly, we must distinguish between position (x) and velocity (v). If an object is at a positive position but has a negative velocity, it doesn't mean it is slowing down; it simply means it is moving back toward the origin.

Scenario	Velocity (v)	Acceleration (a)	Result
Moving Forward, Pushed Forward	+	+	Speeding Up
Moving Backward, Pushed Backward	-	-	Speeding Up
Moving Forward, Braking	+	-	Slowing Down
Moving Backward, Braking	-	+	Slowing Down

Sources: Science-Class VII . NCERT(Revised ed 2025), Measurement of Time and Motion, p.116

7. Relative Position and Motion Toward Origin (exam-level)

To understand the motion of an object relative to a reference point, we must look at the signs of its position (x) and its velocity (v). The origin (x = 0) is our fixed reference. If an object is at a positive position (x > 0) but has a negative velocity (v < 0), it is moving to the left, which means it is approaching the origin. Conversely, if it is at a negative position (x < 0) but has a positive velocity (v > 0), it is moving to the right, also approaching the origin. Therefore, a simple rule for motion toward the origin is that position and velocity must have opposite signs. Moving beyond simple direction, we must distinguish between speeding up and slowing down. This is determined by the relationship between velocity and acceleration (a). A force can change the speed or direction of motion Science, Class VIII, Exploring Forces, p.64. If velocity and acceleration have the same sign, the object is speeding up (acceleration is assisting the motion). If they have opposite signs, the object is slowing down (acceleration is opposing the motion). This is crucial for UPSC physics problems where a particle might be moving toward the origin but simultaneously decelerating.

Motion State	Velocity (v) and Acceleration (a)	Result
Speeding Up	Same Sign (both + or both -)	Magnitude of velocity increases
Slowing Down	Opposite Signs (+ and -)	Magnitude of velocity decreases

A common conceptual trap is the belief that if an object's velocity is zero, its acceleration must also be zero. This is not necessarily true! Consider a ball thrown vertically upward. At the very peak of its flight, its instantaneous velocity is zero, yet it is still under the constant acceleration of gravity (approx. 9.8 m/s²). If acceleration were zero at the peak, the ball would simply hover there forever! However, if velocity remains zero over a finite time interval, then the acceleration must indeed be zero throughout that interval, as there is no change in motion occurring.

Sources: Science, Class VIII (NCERT), Exploring Forces, p.64; Geography Class XI (NCERT), The Origin and Evolution of the Earth, p.20

8. Solving the Original PYQ (exam-level)

Review the concepts above and try solving the question.