All questions of Motion for UPSC CSE Exam

Acceleration in Motion
Accelerated motion refers to an object's motion where its velocity changes over time. This change in velocity can be either an increase or a decrease, indicating acceleration or deceleration, respectively.

Example of Accelerated Motion

• A ball rolling down a slope: When a ball is placed on an inclined plane or slope, gravity pulls it downwards causing it to accelerate. As the ball rolls down the slope, its velocity increases continuously, demonstrating accelerated motion. The rate of acceleration depends on the steepness of the slope and the force of gravity acting on the ball.

Explanation
When the ball is released at the top of the slope, it initially has zero velocity. As gravity acts on the ball, it accelerates due to the force pulling it downward. The ball gains speed as it moves down the slope, and the velocity at any given point is higher than the velocity at the previous point. This continuous increase in velocity indicates accelerated motion.
In contrast, options such as a pendulum swinging back and forth, a car moving at a constant speed on a straight road, and a person walking at a steady pace do not demonstrate accelerated motion. In these cases, the velocity remains constant or changes at a constant rate, without any significant increase or decrease in speed over time.
Therefore, the example of a ball rolling down a slope is the best representation of accelerated motion among the given options.

Newton's Second Law of Motion

Newton's Second Law of Motion states that the acceleration of an object is directly proportional to the force applied to it and inversely proportional to the mass of the object. This law is one of the fundamental principles of physics and is often referred to as F=ma, where F is the force applied to an object, m is the mass of the object, and a is the resulting acceleration.

Explanation:

Direct Proportionality:
When a force is applied to an object, the object will accelerate in the direction of the force. The greater the force applied, the greater the acceleration of the object. This means that the force and acceleration are directly proportional to each other. If the force applied is doubled, the resulting acceleration will also double, and if the force is halved, the acceleration will also be halved.

Inverse Proportionality:
The mass of an object refers to the amount of matter it contains. The greater the mass of an object, the more inertia it has, and the harder it is to accelerate. In other words, the acceleration of an object is inversely proportional to its mass. If the mass of an object is doubled, the resulting acceleration will be halved, and if the mass is halved, the acceleration will be doubled.

Mathematical Formulation:
The relationship between force, mass, and acceleration can be mathematically expressed using Newton's Second Law of Motion:

F = ma

Where:
F = Force applied to the object (in Newtons)
m = Mass of the object (in kilograms)
a = Acceleration of the object (in meters per second squared)

This equation shows that the force applied to an object is directly proportional to its acceleration and inversely proportional to its mass. By rearranging the equation, we can also solve for mass or acceleration when the other two variables are known.

Significance:
Newton's Second Law of Motion is a fundamental principle in physics and has numerous applications in various fields. It helps us understand the relationship between force, mass, and acceleration, providing a basis for studying the motion of objects. This law is essential in fields like engineering, mechanics, and physics, enabling us to calculate and predict the behavior of objects under the influence of forces. It forms the foundation for concepts such as momentum, energy, and power, and plays a crucial role in explaining the laws of motion.

Formula to Calculate Average Speed
Average speed can be calculated using the formula:

Speed = Distance ÷ Time

Explanation:
- Speed: The average speed of an object is the total distance traveled by the object divided by the total time taken to travel that distance.
- Distance: The total distance covered by the object in a given time period.
- Time: The total time taken by the object to cover the given distance.

Example:
If a car travels 100 miles in 2 hours, the average speed can be calculated as follows:
Speed = 100 miles ÷ 2 hours
Speed = 50 miles per hour

Importance of Average Speed:
- Average speed is an essential concept in physics and everyday life to measure how fast an object is moving on average.
- It helps in determining the efficiency of a journey or the rate of change in an object's position over time.

Conclusion:
Calculating average speed using the formula Speed = Distance ÷ Time is crucial in various fields such as physics, engineering, and transportation. It provides valuable information about the motion of objects and helps in analyzing their performance.

Understanding Contact Forces
Contact forces are those that occur when two objects are physically touching each other. In this context, the correct answer is Frictional Force.
Types of Forces
- Magnetic Force:
- Acts at a distance between magnetic objects.
- Does not require physical contact.
- Gravitational Force:
- The force of attraction between two masses.
- Operates over a distance and does not involve contact.
- Electrostatic Force:
- The force between charged particles.
- Also acts at a distance without direct contact.
Frictional Force Explained
- Definition:
- Frictional force is the resistance that one surface or object encounters when moving over another.
- Nature of Force:
- It arises from direct contact between surfaces.
- It can be static (preventing motion) or kinetic (resisting motion during movement).
- Examples:
- When pushing a book across a table, the friction between the book and table resists the motion.
- Walking involves friction between shoes and the ground, allowing for movement.
Conclusion
In summary, the frictional force is the only example of a contact force among the given options. It is essential in everyday activities, enabling motion and preventing slips, while the other forces listed operate without direct contact.

Understanding Inertia
Inertia is a fundamental concept in physics that describes how objects behave in response to forces. It is essential for understanding motion and dynamics.

Definition of Inertia
- Inertia is defined as the tendency of an object to resist any change in its state of motion.
- This means that an object at rest will remain at rest, and an object in motion will continue to move at a constant velocity unless acted upon by an external force.

Key Characteristics of Inertia
- Inertia is not a force; rather, it is a property of matter.
- The amount of inertia an object has is directly related to its mass:
- Heavier objects have greater inertia and require more force to change their motion.
- Lighter objects have less inertia and are easier to accelerate or decelerate.

Examples of Inertia
- When a car suddenly stops, passengers lurch forward. This happens because their bodies have the inertia to continue moving forward despite the car's stop.
- A hockey puck sliding on ice will keep moving in a straight line until friction or another force acts on it.

Conclusion
- Therefore, the correct answer is option 'B': It is the tendency of an object to resist a change in its state of motion.
- Understanding inertia is crucial in the study of physics as it lays the foundation for Newton's first law of motion, which states that an object will remain at rest or in uniform motion unless acted upon by an external force.

Velocity: A Vector Quantity
Velocity is a vector quantity that includes both magnitude and direction. It is different from speed, which is a scalar quantity that only considers the magnitude of motion. Velocity, on the other hand, takes into account the direction of the motion along with its magnitude.

Explanation
- Vector Quantity: A vector quantity is one that has both magnitude and direction. In the case of velocity, the magnitude represents the speed of an object, while the direction indicates the path it is following.
- Example: For instance, if a car is traveling at 60 km/h towards the north, its velocity would be 60 km/h north. If the same car changes its direction to east while maintaining the speed of 60 km/h, its velocity would change to 60 km/h east.
- Importance: The inclusion of direction in velocity is crucial in describing the complete motion of an object. It helps in understanding how an object is moving in a particular direction rather than just knowing its speed.

Conclusion
In conclusion, velocity is a vector quantity that not only includes the magnitude of motion but also the direction in which the object is moving. This distinction from speed makes it an essential parameter in physics and various other fields where understanding the complete motion of an object is necessary.