A car is moving with a uniform speed. However its momentum is changing. Then the car

1. Scalar vs. Vector Quantities (basic)

To understand mechanics, we must first understand how we measure the world. In physics, all physical quantities are divided into two fundamental categories: Scalars and Vectors. A Scalar quantity is one that is described purely by its magnitude (a numerical value and a unit). For instance, if you say it is 35°C outside or that a bag weighs 5 kg, you have given all the necessary information. There is no 'direction' to temperature or mass.

In contrast, a Vector quantity requires both magnitude and direction to be fully understood. Think of a force—if you push a door, the direction in which you push is just as important as how hard you push Science, Class VIII, Exploring Forces, p.77. Common vectors include displacement, velocity, acceleration, and force. A simple way to visualize this is to think of a scalar as a distance (e.g., 10 km) and a vector as a displacement (e.g., 10 km North).

The distinction becomes critical when objects move. While speed is a scalar (how fast an object moves), velocity is its vector counterpart (speed in a specific direction). This means that even if an object moves at a constant speed, its velocity—and consequently its momentum—can change if it simply changes its direction, such as when a car turns a corner or moves in a circular path. This change in direction is what leads to acceleration, even without a change in the speedometer reading.

Feature	Scalar Quantities	Vector Quantities
Definition	Only Magnitude (Size)	Magnitude + Direction
Examples	Mass, Time, Temperature, Speed, Distance	Force, Velocity, Displacement, Momentum
Changes When...	Only the value changes.	The value OR the direction changes.

Sources: Science, Class VIII (NCERT Revised ed 2025), Exploring Forces, p.77

2. Speed vs. Velocity (basic)

In our journey through mechanics, we first need to distinguish between simply "how fast" an object moves and "in what direction" it is headed. Speed is a scalar quantity, meaning it only describes the magnitude or the rate at which an object covers distance. For instance, if a bus moves at 50 km/h, we are discussing its speed Science-Class VII . NCERT(Revised ed 2025), Chapter 8, p.115. However, in physics and for competitive exams like UPSC, magnitude alone often tells only half the story. To get the full picture, we need Velocity.

Velocity is a vector quantity that represents the rate of change of an object's position with respect to time in a specified direction. While speed tells you a car is doing 60 km/h, velocity tells you it is doing 60 km/h towards the North. This distinction is vital: if a car travels at a constant speed but turns a corner, its speed remains the same, but its velocity changes because the direction of motion has altered. This leads us to the concept of uniform motion; an object is in uniform linear motion only if it moves along a straight line at a constant speed Science-Class VII . NCERT(Revised ed 2025), Chapter 8, p.117. If it turns, even at the same speed, its motion is no longer considered uniform in terms of velocity.

Feature	Speed	Velocity
Nature	Scalar (Magnitude only)	Vector (Magnitude + Direction)
Formula	Distance / Time	Displacement / Time
Change	Changes only if the rate of motion changes.	Changes if either speed OR direction changes.

A fascinating application of this is circular or elliptical motion. Imagine a satellite orbiting Earth or a car on a circular track at a steady 40 km/h. Because the direction is constantly curving, the velocity is constantly changing. This change in velocity implies the object is accelerating, even if the speedometer remains fixed! This nuance is why velocity is the foundational component for Momentum (Mass × Velocity); a change in direction alone is enough to change an object's momentum, even if its speed is perfectly uniform.

Sources: Science-Class VII . NCERT(Revised ed 2025), Chapter 8: Measurement of Time and Motion, p.115; Science-Class VII . NCERT(Revised ed 2025), Chapter 8: Measurement of Time and Motion, p.117

3. Newton’s Second Law and Linear Momentum (intermediate)

To understand Newton’s Second Law, we must first master the concept of Linear Momentum (p). Momentum is often described as the 'quantity of motion' an object possesses. Mathematically, it is the product of an object's mass (m) and its velocity (v), expressed as p = mv. While mass is a scalar, velocity is a vector—meaning it has both magnitude (speed) and direction. Consequently, momentum is also a vector quantity. This is a crucial distinction: even if an object’s speed remains the same, its momentum changes if it changes direction, such as when a car rounds a curve.

Newton’s Second Law states that the Force (F) acting on an object is equal to the rate of change of its momentum over time. In simpler terms, to change how fast an object moves or the direction it is traveling, you must apply a force. The SI unit for this force is the newton (N) Science, Class VIII NCERT, Exploring Forces, p.65. When we talk about uniform linear motion, we refer to an object moving along a straight line at a constant speed Science-Class VII NCERT, Measurement of Time and Motion, p.117. In this specific state, because neither the speed nor the direction changes, the momentum is constant, and the net external force is zero.

However, motion in the real world is rarely that simple. Most movements are non-uniform, where the speed or direction fluctuates Science-Class VII NCERT, Measurement of Time and Motion, p.119. A fascinating example is found in planetary motion. According to Kepler’s Second Law, a planet's orbital speed is not constant; it increases as it nears the Sun (perigee) and decreases as it recedes (apogee) Physical Geography by PMF IAS, The Motions of The Earth and Their Effects, p.257. Because both the speed and the direction of the planet are constantly shifting along its elliptical path, its linear momentum is always changing, signifying that gravitational force is continuously acting upon it.

Concept	Uniform Linear Motion	Non-Uniform/Curved Motion
Speed	Constant	Variable (usually)
Direction	Fixed (Straight line)	Changing
Momentum	Constant	Changing (Vector changes)

Sources: Science, Class VIII NCERT, Exploring Forces, p.65; Science-Class VII NCERT, Measurement of Time and Motion, p.117; Science-Class VII NCERT, Measurement of Time and Motion, p.119; Physical Geography by PMF IAS, The Motions of The Earth and Their Effects, p.257

4. Centripetal Force and Curved Motion (intermediate)

To understand motion in the real world, we must distinguish between speed and velocity. While speed tells us how fast an object moves, velocity is a vector quantity, meaning it includes both speed and the specific direction of travel Science-Class VII . NCERT(Revised ed 2025), Chapter 8: Measurement of Time and Motion, p. 117. This distinction is crucial because even if a car maintains a steady speed of 60 km/h, its velocity changes the moment the steering wheel is turned. This change in direction implies that the object is accelerating, a concept known as centripetal acceleration.

Centripetal force is the "center-seeking" force that keeps an object moving along a curved or circular path. It acts at right angles to the direction of motion, pulling the object toward the center of the curve Physical Geography by PMF IAS, Pressure Systems and Wind System, p. 309. Without this inward pull, the object’s inertia would carry it away in a straight line. For example, when a car enters a curve, the friction between the tires and the road provides the centripetal force necessary to change the car's direction. In the atmosphere, this force is what creates the vortex or circular flow of winds around low and high-pressure centers, resulting in cyclones and anticyclones.

Because momentum is the product of mass and velocity (p = mv), it is also a vector. This leads to a fascinating conclusion: an object moving at a uniform speed on a curved path (like an elliptical orbit or a circular track) actually has changing momentum. Even though the magnitude (speed) is constant, the direction of the velocity vector is continuously being altered by the centripetal force. This is why most motion we observe in daily life—whether it is a child swinging a bag or a planet orbiting a star—is technically non-uniform motion because the direction of travel is rarely a perfectly straight line for long Science-Class VII . NCERT(Revised ed 2025), Chapter 8: Measurement of Time and Motion, p. 119.

Sources: Science-Class VII . NCERT(Revised ed 2025), Chapter 8: Measurement of Time and Motion, p.117, 119; Physical Geography by PMF IAS, Pressure Systems and Wind System, p.309

5. Kepler’s Laws and Elliptical Orbits (intermediate)

To understand how celestial bodies move, we must look at Kepler’s Laws of Planetary Motion. For centuries, it was believed that planets moved in perfect circles, but Johannes Kepler discovered that the orbit of a planet is an ellipse, with the Sun situated at one of the two foci Physical Geography by PMF IAS, The Solar System, p.21. An ellipse is essentially a 'stretched' circle, meaning the distance between the Earth and the Sun is constantly changing. We call the point where the Earth is closest to the Sun the perihelion (occurring around January 3rd), and the point where it is farthest the aphelion (occurring around July 4th) Physical Geography by PMF IAS, The Motions of The Earth and Their Effects, p.255.

The second law, often called the Law of Equal Areas, tells us that a line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time. This has a profound implication for a planet's orbital velocity: to sweep out the same 'area' of space when it is far away (at the apogee/aphelion) versus when it is close (at the perigee/perihelion), the planet must change its speed. Specifically, the speed of the planet increases as it nears the sun and decreases as it recedes Physical Geography by PMF IAS, The Motions of The Earth and Their Effects, p.257. This variation in speed is why the Northern Hemisphere experiences a slightly longer summer (about 92 days) than winter (about 89 days); because the Earth is farther from the Sun during the northern summer, it moves more slowly along its orbit Physical Geography by PMF IAS, The Motions of The Earth and Their Effects, p.256.

From a physics perspective, this motion is a perfect example of non-uniform motion. Even if a planet's speed were constant, its momentum would still be changing because momentum is a vector quantity (mass × velocity). Since the planet is moving along a curved, elliptical path, its direction is continuously altering. This change in direction implies a change in velocity, which means the planet is constantly experiencing centripetal acceleration directed toward the Sun. Kepler’s third law ties this all together by stating that the time it takes to complete an orbit (the period) is mathematically linked to the size of the orbit: specifically, the square of the orbital period (T²) is proportional to the cube of the semi-major axis (a³) Physical Geography by PMF IAS, The Solar System, p.21.

Sources: Physical Geography by PMF IAS, The Solar System, p.21; Physical Geography by PMF IAS, The Motions of The Earth and Their Effects, p.255-257

6. Momentum Change via Directional Shift (exam-level)

To understand momentum fully, we must look beyond just how fast an object is moving. Momentum is a vector quantity, defined mathematically as the product of mass and velocity (p = mv). While mass is a scalar, velocity is a vector—meaning it possesses both magnitude (speed) and a specific direction. Because momentum is tied to velocity, any change in the direction of motion results in a change in momentum, even if the speed remains perfectly constant Science-Class VII, Measurement of Time and Motion, p.117. In our daily experience, we often equate 'acceleration' or 'change' only with speeding up or slowing down. However, in physics, a change in the direction of motion is just as significant as a change in speed. For instance, if a car travels at a steady 60 km/h but enters a sharp curve, its velocity vector is rotating. Since the direction is shifting, the velocity is changing; therefore, the momentum is changing. This explains why a force is required to turn a vehicle—force is necessary to change momentum, whether that change is in magnitude or direction Science, Class VIII, Exploring Forces, p.64.

Feature	Uniform Linear Motion	Uniform Circular/Elliptical Motion
Speed	Constant	Constant
Direction	Fixed (Straight line)	Continuously Changing
Momentum	Constant	Changing

This principle is vital when observing objects in curved paths, such as planets in elliptical orbits or athletes on a circular track. Even if they maintain a 'uniform speed,' they are in a state of non-uniform motion in a vector sense because their direction—and thus their momentum—is in constant flux. Unlike light, which changes direction when moving between media due to speed changes Science, Class X, Light – Reflection and Refraction, p.148, a physical object changing direction at a constant speed proves that momentum is inherently directional.

Sources: Science-Class VII . NCERT(Revised ed 2025), Measurement of Time and Motion, p.117; Science ,Class VIII . NCERT(Revised ed 2025), Exploring Forces, p.64; Science , class X (NCERT 2025 ed.), Light – Reflection and Refraction, p.148

7. Solving the Original PYQ (exam-level)

This question perfectly synthesizes your recently learned concepts regarding scalar and vector quantities. You have already mastered the fact that momentum is a vector, calculated as the product of mass and velocity. The core of this problem lies in the distinction between speed and velocity: while the car maintains a uniform speed (magnitude), the 100% vector nature of momentum means that even if the speed stays the same, a change in direction will cause the momentum to change. Therefore, to solve this, you must look for a scenario where the direction is not constant.

Walking through the logic, since the car has uniform speed but changing momentum, it must be changing its direction of travel. This leads us directly to the conclusion that the car (A) may be on an elliptical path (or any curved path), where the velocity vector is constantly rotating even if its length (speed) remains fixed. This motion is a form of acceleration—specifically centripetal acceleration—because any change in the velocity vector, whether in magnitude or direction, constitutes acceleration as per Science-Class VII . NCERT(Revised ed 2025).

UPSC often uses options (B) and (C) as traps to test if you confuse uniform speed with uniform velocity. A straight path (B) with no acceleration would mean constant momentum, which contradicts the question. A straight path with acceleration (C) would require the speed to change, which also contradicts the premise of "uniform speed." Finally, option (D) is a conceptual impossibility; if momentum is changing, the velocity is changing, and by definition, the car must be accelerating. Always remember: constant speed does not mean constant momentum if the path is curved.