9th Physics Federal Board Notes: Unit 2 Kinematics
📋 Table of Contents
- 1. Multiple Choice Questions
- 2. Short Response Questions
- 2.1 Motion of Ferris Wheel
- 2.2 Zero Displacement with Non-Zero Distance
- 2.3 Direction of Velocity in Circular Motion
- 2.4 Acceleration Without Speed Change
- 2.5 Acceleration Opposite to Motion
- 2.6 Acceleration in Daily Life
- 2.7 Distance-Time Graph Analysis
- 2.8 Car Controls for Acceleration
- 2.9 Falling Objects with Different Masses
- 2.10 Acceleration of Falling Objects
- 3. Long Response Questions
🔬 Introduction to Unit 2: Kinematics
Unit 2: Kinematics explores the fundamental concepts of motion without considering the forces that cause it. This unit helps students understand how objects move, how to describe their motion mathematically, and how to interpret motion through graphs. You'll learn about displacement, velocity, acceleration, and the equations that govern motion under constant acceleration.
1. Multiple Choice Questions
Displacement is defined as the change in position of an object from its initial point to its final point. It is a vector quantity that considers both magnitude and direction.
The screw of a rotating fan undergoes rotatory motion as it spins around its own axis while the fan blades move in a circular path.
When an object is decelerating, its acceleration is in the opposite direction to its motion. Since the cyclist is moving westward, the acceleration is eastward.
Total distance = \(3 \, \text{km} + 4 \, \text{km} = 7 \, \text{km}\)
Displacement = \(\sqrt{(3)^2 + (4)^2} = \sqrt{9 + 16} = \sqrt{25} = 5 \, \text{km}\) (southwest direction)
Total displacement = \(60 \, \text{m} - 30 \, \text{m} = 30 \, \text{m}\) to the right
Total time = \(3 \, \text{s} + 2 \, \text{s} = 5 \, \text{s}\)
Average velocity = \(\frac{\text{Total displacement}}{\text{Total time}} = \frac{30}{5} = 6 \, \text{m/s}\)
Change in velocity = acceleration × time
= \(2 \, \text{m/s}^2 × 5 \, \text{s} = 10 \, \text{m/s}\)
Using the equation: \(v = u + at\)
= \(10 \, \text{m/s} + (2 \, \text{m/s}^2 × 10 \, \text{s})\)
= \(10 + 20 = 30 \, \text{m/s}\)
The slope of a displacement-time graph represents velocity. When the slope increases, it means the velocity is increasing, indicating acceleration.
At the top of its path, the ball's velocity is zero, but it still experiences gravitational acceleration of 9.8 m/s² downward.
The slope of a distance-time graph represents speed, which is the rate of change of distance with respect to time.
The area under a speed-time graph represents the total distance covered by the object during the time interval.
Acceleration = Change in velocity / Time
= \(20 \, \text{m/s} / 5 \, \text{s} = 4 \, \text{m/s}^2\)
Using the equation: \(v = u + gt\)
= \(0 + (9.8 \, \text{m/s}^2 × 4 \, \text{s})\)
= \(39.2 \, \text{m/s}\)
A curved line with increasing slope in a distance-time graph indicates that the object is covering more distance in equal time intervals, meaning its speed is increasing.
2. Short Response Questions
In a park, children are enjoying a ride on Ferris wheel as shown. What kind of motion the big wheel has and what kind of motion the riders have?
🎡 Motion of Ferris Wheel
The big wheel of the Ferris wheel undergoes rotatory motion as it rotates around its fixed central axis. This is similar to how a wheel spins around its axle.
The riders, on the other hand, experience circular motion because they move in a circular path around the center of the wheel while sitting in their seats. Though each rider follows a circular trajectory, their motion is actually a combination of circular and periodic motion.
A boy moves for some time, give two situations in which his displacement is zero but covered distance is not zero?
🚶 Zero Displacement with Non-Zero Distance
Displacement is zero when the initial and final positions are the same, regardless of the path taken. Here are two common situations:
- Circular Path: The boy walks in a complete circle and returns to his starting point. The total distance covered equals the circumference of the circle, but his displacement is zero because his final position matches his starting position.
- Round Trip: The boy walks forward a certain distance and then returns along the same path back to his starting point. The distance covered is twice the distance of one leg of the journey, but displacement is zero as he ends up where he began.
A stone tied to a string is whirling in a circle, what is the direction of its velocity at any instant?
🌀 Direction of Velocity in Circular Motion
The direction of the stone's velocity at any instant is tangent to the circular path at that specific point. This means the velocity vector is perpendicular to the radius of the circle at that position and points in the direction of motion.
As the stone moves around the circle, the direction of its velocity continuously changes, even if its speed remains constant. This constant change in direction is what causes the centripetal acceleration that keeps the stone moving in a circular path.
Is it possible to accelerate an object without speeding it up or slowing it down?
⚡ Acceleration Without Speed Change
Yes, it is possible to accelerate an object without changing its speed. This occurs when the object's direction of motion changes while its speed remains constant.
The most common example is uniform circular motion, where an object moves at constant speed along a circular path. Even though the speed doesn't change, the object is constantly accelerating because its velocity (a vector with both magnitude and direction) is changing due to the continuous change in direction.
This type of acceleration is called centripetal acceleration and is always directed toward the center of the circular path.
Can a car moving towards the right have a direction of acceleration towards the left?
🚗 Acceleration Opposite to Motion
Yes, a car moving toward the right can have acceleration directed toward the left. This occurs when the car is decelerating or slowing down.
When the acceleration vector points in the direction opposite to the velocity vector, the object slows down. In this case, the car's velocity is to the right, but its acceleration is to the left, causing it to gradually reduce its speed.
This is a common situation when a driver applies brakes while moving forward - the car continues moving forward but is accelerating backward (decelerating).
With the help of daily life examples, describe the situations in which:
a. Acceleration is in the direction of motion
Example: A car speeding up while moving forward on a straight road. When you press the accelerator pedal, the car moves faster in the direction it's already traveling, so acceleration is in the same direction as motion.
b. Acceleration is against the direction of motion
Example: A bicycle slowing down when brakes are applied. As the cyclist squeezes the brake levers, the bicycle continues moving forward but is accelerating backward (decelerating), reducing its speed.
c. Acceleration is zero, and the body is in motion
Example: A train moving at constant speed on a straight track. When a train maintains a steady velocity (constant speed and direction), its acceleration is zero even though it's clearly in motion.
Examine distance-time graph of a motorcyclist (as shown), what does this graph tell us about the speed of motorcyclist? Is he moving with uniform speed or not?
📈 Distance-Time Graph Analysis
Based on the distance-time graph shown, we can determine that the motorcyclist is not moving with uniform speed.
Here's how we can tell:
- The graph shows a curved line rather than a straight line
- The slope of the graph is changing at different points
- Since speed is represented by the slope of a distance-time graph, a changing slope indicates changing speed
Specifically, the increasing steepness of the curve suggests that the motorcyclist is accelerating - covering more distance in each successive time interval, meaning the speed is increasing over time.
A car is moving on a straight road. What controls in the car produce acceleration and what controls produce deceleration?
🚘 Car Controls for Acceleration
In a car moving on a straight road:
- Acceleration is produced by: The accelerator pedal (gas pedal). When pressed, it increases fuel flow to the engine, generating more force that causes the car to speed up in the direction of motion.
- Deceleration is produced by: The brake pedal. When applied, it creates friction that opposes the car's motion, causing it to slow down. Additionally, simply releasing the accelerator pedal also produces deceleration due to air resistance and friction.
Both controls change the car's velocity - the accelerator increases it, while the brakes decrease it. Even maintaining constant speed requires balancing these controls against resistive forces.
Two objects of different masses are dropped from the top of a building at the same time. Which one will hit the ground first?
🏢 Falling Objects with Different Masses
In the absence of air resistance, both objects will hit the ground at the same time, regardless of their masses.
This is because the acceleration due to gravity is constant for all objects near the Earth's surface (approximately 9.8 m/s²), and this acceleration is independent of mass. The equation for the time of fall is:
Where h is the height and g is the acceleration due to gravity. Since neither h nor g depends on mass, the time of fall is the same for both objects.
In reality, with air resistance, lighter objects with larger surface areas might fall slightly slower, but in ideal conditions (vacuum), they fall together.
What is the acceleration of a body falling freely called?
⬇️ Acceleration of Falling Objects
The acceleration of a body falling freely under the influence of gravity is called acceleration due to gravity, denoted by the symbol g.
This acceleration has the following characteristics:
- Its standard value near the Earth's surface is approximately 9.8 m/s²
- It is directed vertically downward toward the center of the Earth
- It is constant for all objects regardless of their mass (in the absence of air resistance)
- It varies slightly with altitude and geographical location
This acceleration causes freely falling objects to increase their downward velocity by about 9.8 m/s every second during their fall.
3. Long Response Questions
Define rest and motion. Also give examples.
🛑 Rest and Motion
In physics, rest and motion are relative concepts that describe the position of an object in relation to its surroundings.
Rest
A body is said to be at rest if it does not change its position with respect to its surroundings with the passage of time.
Examples:
- A book lying on a table
- A parked car
- A building relative to the ground
- A person sitting in a stationary chair
Motion
A body is said to be in motion if it changes its position with respect to its surroundings with the passage of time.
Examples:
- A moving car on a road
- A flying bird
- A swinging pendulum
- A person walking
💡 Important Note
Rest and motion are relative terms. An object may be at rest relative to one reference point but in motion relative to another. For example, a passenger sitting in a moving train is at rest relative to the train but in motion relative to the ground outside.
Explain different types of motion with examples.
🔄 Types of Motion
Motion can be classified into several types based on the path followed by the moving object. Understanding these types helps in analyzing and describing movement in the physical world.
Translatory Motion
Motion in which all points of a moving body move uniformly in the same direction along parallel paths.
Examples:
- A car moving on a straight road
- A bullet fired from a gun
- A train moving on straight tracks
Rotatory Motion
Motion in which a body rotates about a fixed axis, with different points moving in circles of different radii.
Examples:
- The spinning of Earth on its axis
- A rotating fan
- A spinning top
Vibratory Motion
Motion in which a body moves to and fro about a fixed point (mean position) in a periodic manner.
Examples:
- The motion of a pendulum
- A guitar string when plucked
- A mass attached to a spring
Circular Motion
Motion in which a body moves along a circular path with a fixed center.
Examples:
- A stone whirled in a circle
- Motion of Earth around the Sun
- A car turning around a circular track
Random Motion
Irregular motion with no specific pattern or direction.
Examples:
- Motion of gas molecules
- Movement of insects
- Brownian motion of particles
Oscillatory Motion
Motion that repeats itself in equal intervals of time about a mean position.
Examples:
- Swinging of a pendulum
- Vibration of a tuning fork
- Motion of a swing
Differentiate between scalar and vector quantities with examples.
| Aspect | Scalar Quantities | Vector Quantities |
|---|---|---|
| Definition | Quantities that have only magnitude (size) but no direction | Quantities that have both magnitude and direction |
| Representation | Represented by a number with appropriate unit | Represented by an arrow where length shows magnitude and direction shows direction |
| Mathematical Operations | Follow ordinary algebra rules | Follow vector algebra rules |
| Examples |
|
|
Differentiate between position, distance and displacement.
| Concept | Definition | Nature | Example |
|---|---|---|---|
| Position | The location of an object relative to a reference point | Vector quantity (has direction) | A car is 5 km East of the city center |
| Distance | The total path length traveled by an object | Scalar quantity (magnitude only) | A person walks 3 km to school and 3 km back home, total distance = 6 km |
| Displacement | The shortest straight-line distance from initial to final position | Vector quantity (magnitude and direction) | A person walks 3 km East to school and 3 km West back home, displacement = 0 |
📏 Key Differences
- Distance is always positive or zero, while displacement can be positive, negative, or zero
- Distance depends on the path taken, while displacement depends only on initial and final positions
- Distance is always greater than or equal to the magnitude of displacement
- For motion in a straight line without change in direction, distance equals the magnitude of displacement
Differentiate between speed and velocity.
| Aspect | Speed | Velocity |
|---|---|---|
| Definition | Rate of change of distance | Rate of change of displacement |
| Nature | Scalar quantity (magnitude only) | Vector quantity (magnitude and direction) |
| Formula | Speed = Total distance / Time | Velocity = Displacement / Time |
| Possible Values | Always positive or zero | Can be positive, negative, or zero |
| Dependence on Path | Depends on the actual path taken | Independent of path, depends only on initial and final positions |
| Example | A car travels 60 km in 1 hour, speed = 60 km/h | A car travels 60 km East in 1 hour, velocity = 60 km/h East |
📊 Types of Speed and Velocity
Uniform Speed: When a body covers equal distances in equal intervals of time, regardless of direction.
Variable Speed: When a body covers unequal distances in equal intervals of time.
Average Speed: Total distance traveled divided by total time taken.
Instantaneous Speed: Speed at a particular instant of time.
Uniform Velocity: When a body has constant speed and constant direction.
Variable Velocity: When either speed or direction (or both) changes with time.
What are freely falling bodies? Prove that acceleration of all the freely falling bodies is the same.
⬇️ Freely Falling Bodies
Freely falling bodies are objects moving under the influence of gravity alone, with no other forces acting on them (neglecting air resistance).
🧪 Proof: Same Acceleration for All Freely Falling Bodies
According to Newton's Second Law of Motion:
The force of gravity acting on a body (its weight) is given by:
Where:
- F = Force of gravity (weight)
- m = Mass of the object
- g = Acceleration due to gravity
Equating both expressions for force:
Dividing both sides by m:
This shows that the acceleration (a) of a freely falling body equals the acceleration due to gravity (g), which is approximately 9.8 m/s² near the Earth's surface.
Since mass (m) cancels out in the equation, the acceleration is the same for all objects regardless of their mass, provided air resistance is negligible.
🔍 Experimental Verification
Galileo famously demonstrated this principle by dropping objects of different masses from the Leaning Tower of Pisa. In a vacuum (where there is no air resistance), a feather and a hammer fall at the same rate, as demonstrated by Apollo astronauts on the Moon.
Explain distance-time graph for bodies moving with uniform and non-uniform speed.
📈 Distance-Time Graphs
Distance-time graphs provide a visual representation of an object's motion, showing how distance changes with time. The slope of these graphs gives information about the object's speed.
Uniform Speed
When a body moves with uniform speed (constant speed):
- The distance-time graph is a straight line
- The slope of the line is constant
- Speed = Slope of the graph
- Greater slope indicates greater speed
Example: A car moving at a constant speed of 60 km/h would show a straight line on a distance-time graph.
Non-Uniform Speed
When a body moves with non-uniform speed (changing speed):
- The distance-time graph is a curved line
- The slope of the curve changes at different points
- Instantaneous speed = Slope of tangent at that point
- Increasing slope indicates acceleration
- Decreasing slope indicates deceleration
Example: A car starting from rest and gradually increasing its speed would show a curve with increasing slope.
📊 Interpreting Distance-Time Graphs
Horizontal Line: Object is at rest (zero speed)
Straight Line with Constant Slope: Object moving with uniform speed
Curved Line with Increasing Slope: Object accelerating (speed increasing)
Curved Line with Decreasing Slope: Object decelerating (speed decreasing)
Steeper Slope: Higher speed
Gentler Slope: Lower speed
Explain speed-time graph for bodies moving with uniform and variable speed.
📊 Speed-Time Graphs
Speed-time graphs show how an object's speed changes with time. These graphs provide information about acceleration and the distance traveled.
Uniform Speed
When a body moves with uniform speed (constant speed):
- The speed-time graph is a horizontal straight line parallel to the time axis
- Acceleration = 0 (since speed is not changing)
- Distance covered = Area under the graph = Speed × Time
Example: A car cruising at a constant 80 km/h would show a horizontal line at the 80 km/h mark.
Uniform Acceleration
When a body moves with uniform acceleration (constant acceleration):
- The speed-time graph is a straight line with constant slope
- Acceleration = Slope of the graph
- Positive slope indicates positive acceleration (speeding up)
- Negative slope indicates negative acceleration (slowing down)
- Distance covered = Area under the graph
Example: A car accelerating uniformly from rest would show a straight line with positive slope.
Variable Acceleration
When a body moves with variable acceleration (changing acceleration):
- The speed-time graph is a curved line
- Instantaneous acceleration = Slope of tangent at that point
- Distance covered = Area under the graph
Example: A car with changing acceleration would show a curved line on the speed-time graph.
📐 Calculating from Speed-Time Graphs
Acceleration: Slope of the speed-time graph
Distance: Area under the speed-time graph
For uniform motion: Distance = Speed × Time (area of rectangle)
For uniformly accelerated motion: Distance = Average speed × Time = \(\frac{u + v}{2} × t\) (area of trapezium)
📚 Master 9th Physics Kinematics
Understanding kinematics is fundamental to physics as it forms the basis for studying dynamics and other advanced topics. Practice these concepts with numerical problems and graph interpretations to strengthen your understanding.
Explore More 9th Physics Notes© House of Physics | 9th Physics Federal Board Notes: Unit 2 Kinematics
Comprehensive study guide based on Federal Board curriculum with additional insights from educational resources
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