All questions of Motion for UPSC CSE Exam

Conservation of Momentum in Collisions
The law of conservation of momentum states that the total momentum of a system remains constant if no external forces act on it. This law is particularly applicable to collisions between objects.
Explanation:
- **Before the collision:** In a collision between objects, each object has its own initial momentum. The total momentum of the system is the sum of the individual momenta of the objects before the collision.
- **During the collision:** When the objects collide, they exert forces on each other which may change their individual momenta. However, the law of conservation of momentum states that the total momentum of the system (sum of individual momenta) remains constant during the collision, regardless of the forces involved.
- **After the collision:** After the collision, the objects may have different momenta compared to their initial momenta. However, the total momentum of the system (sum of individual momenta) remains the same as it was before the collision.
Example:
- In a head-on collision between two cars, the total momentum of the system (both cars) before the collision is equal to the total momentum of the system after the collision, provided no external forces like friction or air resistance are present.
Conclusion:
The law of conservation of momentum is a fundamental principle in physics that is especially applicable to collisions between objects. It helps in understanding and predicting the behavior of objects during collisions and reinforces the concept that momentum is conserved in isolated systems.

Explanation:

Newton's first law of motion, also known as the law of inertia, states that an object will remain at rest or in uniform motion unless acted upon by an external force. This law provides the foundation for understanding the behavior of objects in motion.

Definition of Newton's first law:
- An object at rest tends to stay at rest, and an object in motion tends to stay in motion with the same speed and in the same direction, unless acted upon by an external force.

Key points:

1. Rest: If an object is at rest, it will remain at rest unless a force is applied to it. This means that the object resists changes in its state of motion and requires an external force to start moving.

2. Uniform motion: If an object is in motion with a constant velocity, it will continue moving in the same direction and at the same speed unless acted upon by an external force. The object's inertia keeps it moving without any external influence.

3. Inertia: Inertia is the property of an object that resists changes in its state of motion. The greater the mass of an object, the greater its inertia. Objects with more mass require more force to change their state of motion.

4. External force: An external force is any force that is applied to an object from an outside source. It can be a push, a pull, or any other interaction between objects. The presence of an external force is necessary to change the state of motion of an object.

Example:
Consider a book placed on a table. The book remains at rest until an external force, such as a push or a pull, is applied to it. Once the book is set in motion, it will continue moving in a straight line at a constant speed unless acted upon by another force, such as friction or gravity.

Conclusion:
Newton's first law of motion, or the law of inertia, states that an object will remain at rest or in uniform motion unless acted upon by an external force. This law helps explain the behavior of objects in motion and is fundamental to our understanding of mechanics.

Definition of Motion:
Motion is defined as the change in position of an object with respect to time. It involves the concept of an object's location changing over a period of time.

Explanation:
- Change in Position: Motion refers to the displacement or change in position of an object as time progresses. This change can be in any direction and can be measured in terms of distance covered or the displacement from the starting point.
- With Respect to Time: Motion is always described with reference to time. It indicates how the position of an object changes over a specific period, whether it is moving at a constant speed, accelerating, or decelerating.
- Relation to Object: Motion is directly related to the object itself and how it moves through space. It does not depend on external factors like forces applied or the mass of the object.
- Characteristics: The key characteristics of motion include speed, velocity, acceleration, and distance traveled. These parameters help in describing and measuring the motion of an object accurately.
- Importance: Understanding motion is essential in various fields such as physics, engineering, and astronomy. It helps in predicting the behavior of objects, designing systems, and analyzing complex movements.
In conclusion, motion can be best defined as the change in position of an object with respect to time. It is a fundamental concept in physics that explains how objects move and interact with their surroundings.

Terminal Velocity

Terminal velocity is the maximum velocity that an object can reach when falling through a fluid, such as air or water. It occurs when the force of gravity pulling the object downwards is equal to the force of air resistance pushing against it. At terminal velocity, the net force on the object becomes zero, resulting in a constant velocity.

Statement and Explanation

The correct statement about terminal velocity is option 'C': It is the velocity at which air resistance is equal to the weight of the object. This means that the force of air resistance acting on the object is equal in magnitude to the force of gravity pulling it downwards.

Explanation of the Correct Statement

1. Terminal velocity and Air Resistance: Terminal velocity is determined by the balance between the force of gravity and the force of air resistance. As an object falls through a fluid, such as air, it experiences a resistance force due to air molecules colliding with it. This force of air resistance increases with the speed of the object.
2. Weight of the Object: The weight of an object is the force of gravity acting on it. It is determined by the mass of the object and the acceleration due to gravity. The weight of an object is always directed downwards.
3. Equal Forces: At terminal velocity, the force of air resistance acting on the object becomes equal in magnitude to the weight of the object. This means that the object experiences an equal and opposite force to its weight, resulting in a net force of zero.
4. Zero Net Force: When the net force on an object is zero, it no longer accelerates and its velocity becomes constant. This constant velocity is known as the terminal velocity.
5. Mass and Terminal Velocity: The mass of the object does not directly affect the terminal velocity. Terminal velocity depends on the balance between the forces of gravity and air resistance, not the mass of the object. Objects with different masses but the same shape and size will have the same terminal velocity.
6. Maximum Velocity in Free Fall: Option 'A' states that terminal velocity is the maximum velocity an object can reach in free fall. This statement is incorrect because terminal velocity only applies when there is a fluid (such as air) present to provide resistance. In a vacuum or when free falling without air resistance, there is no terminal velocity and the object will continue to accelerate.

Therefore, option 'C' is the correct statement about terminal velocity: It is the velocity at which air resistance is equal to the weight of the object.

Understanding Non-Uniform Motion
Non-uniform motion refers to the movement of an object where its speed and/or direction changes over time. In this context, let's analyze the options provided and identify why option 'B' is the correct example of non-uniform motion.
Analyzing the Options
- Option A: A train moving at a constant speed on a straight track
This describes uniform motion since the train's speed does not change.
- Option B: A car slowing down at a traffic light
This is an example of non-uniform motion. The car is changing its speed as it approaches the traffic light, indicating that its motion is not constant.
- Option C: A satellite orbiting the Earth
Although the satellite travels in a curved path, its speed remains constant. Therefore, this motion can be classified as uniform in terms of speed.
- Option D: A boat sailing smoothly on a calm lake
This scenario also depicts uniform motion, as the boat is moving at a steady pace without any changes in speed or direction.
Conclusion
In summary, option 'B' is the correct answer because:
- The car's speed is decreasing as it approaches a stop, demonstrating non-uniform motion.
- The other options depict scenarios of uniform motion where speed is constant.
Recognizing these distinctions is crucial for understanding the principles of motion, especially in preparation for exams like the Delhi Police Constable test.

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.

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.

Surface area and temperature:
Friction between two surfaces is affected by surface area and temperature.
- Surface area: The amount of friction between two surfaces is directly proportional to the surface area in contact. A larger surface area in contact leads to a greater amount of friction. This is why it is easier to slide a book on a table than a piece of paper, as the book has more surface area in contact with the table.
- Temperature: Temperature can also affect friction. Generally, an increase in temperature can reduce friction between two surfaces. This is because at higher temperatures, the surfaces may expand slightly, reducing the contact area and hence reducing the friction.
Therefore, surface area and temperature are important factors that influence the amount of friction between two surfaces. Understanding these factors is crucial in various fields such as engineering, physics, and material science.