Class 9th Motion Notes PDF

# Class 9th MOTION “Prashant Bhaiya” ## Topics to be covered * Motion * Distance and Displacement * Speed and Velocity * Uniform and Non-Uniform Motion ## Motion * An object is said to be in **motion** when its position changes with time. * To describe the position of an object, we need a refere...

# Class 9th MOTION “Prashant Bhaiya” ## Topics to be covered * Motion * Distance and Displacement * Speed and Velocity * Uniform and Non-Uniform Motion ## Motion * An object is said to be in **motion** when its position changes with time. * To describe the position of an object, we need a reference point or origin. * **e.g.** - Movement of dust, leaves, and branches. - Phenomena of sunrise, sunset, and changing seasons are due to Earth's motion. ## Rest * A body is said to be in a state of **rest** when its position does not change with time. * **e.g.** - Sleeping, sitting, standing, lying. ## Motion is Relative A body can be moving for one observer, and at the same time at rest for another observer. **Example:** For example, a person sitting in an airplane is at zero velocity relative to the airplane but is moving at the same velocity as the airplane with respect to the ground. ## Physical Quantity * A physical quantity is a property of a material or system that can be measured and quantified. * **For example:** mass, represented by the symbol m, can be quantified as m = n kg, where n is the numerical value which is called magnitude and kg is the unit symbol. | Scalar Quantity | Vector Quantity | | -------------------------- | --------------------------- | | It is the physical quantity having own magnitude but no direction. | It is the physical quantity that requires both magnitude and direction. | | **Example:** distance, speed. | **Example:** displacement, velocity. | ## Distance and Displacement  ## Distance vs Displacement | DISTANCE | DISPLACEMENT | | ---------- | --------------- | | Distance is the actual length of the path travelled by the particle in a given interval of time. | Displacement is the shortest distance between the initial position and the final position of the moving particle in a particular direction. | | Distance travelled by the particle in a given interval of time is always positive. | Displacement of the particle in a given interval of time may be positive, negative, or zero. | | Distance travelled by the particle depends upon the path followed by the particle in going from initial position to the final position. | The displacement of the particle between initial position and final position of the particle does not depend upon the path followed by it. | | Distance is scalar quantity | Displacement is a vector quantity. |  ## Speed m/s Km/h Speed is the distance travelled by an object in unit time. If a body covers a certain distance in a certain amount of time, its speed is given by: $s = \frac{d}{t}$. | Speed = | Distance | Time | | :------- | :-------- | :---- | | | | | SI unit of speed is meters per second (m/s). Commercial unit: km/hr **Average speed** is stated as the distance covered by the object within a period of time. **Average speed = Total distance travelled / Total time taken** ## Velocity ($V = \frac{s}{t}$) The Rate of change of displacement is velocity or Velocity is the speed of an object moving in a definite direction. It is a vector quantity. Here, the direction of motion is specified. | Velocity = | Displacement | Time | | :-------- | :------------ | :---- | | | | | SI unit is meters per second (m/s). Commercial unit: km/hr For an object moving along a straight line at a variable speed, average velocity expresses the magnitude of its rate of motion. When the velocity of an object changes at a uniform rate, average velocity is the arithmetic mean of initial and final velocities for a given time period. **Average velocity = (Initial velocity + Final velocity) / 2 = (u + v) / 2** ## Difference between Speed & Velocity | Basis of Comparison | Speed | Velocity | | --------------------- | ------------------------------------------------------------------------ | ----------------------------------------------------------------------------------------------- | | Meaning | It is the rate at which a particular distance is covered by an object. | Velocity refers to the rate at which an object changes their position in a particular direction. | | Quantity | It is a scalar quantity. | Velocity is a vector quantity. | | Indication | Speed indicates how fast an object is moving. | It indicates how fast the object is moving along with its position. | | Value | Speed may never be zero or negative. | Velocity may be zero, negative, or positive. | | Calculation | Speed = Distance / Time | Velocity = Displacement / Time | ## Acceleration Acceleration is seen in non-uniform motion and it can be defined as the rate of change of velocity with time. **Acceleration = Change in velocity / Time taken** It is a vector quantity SI Unit: m/s² If velocity changes from u to v in time t: **a = (v - u) / t** * **Positive acceleration:** Direction of velocity. * **Negative acceleration:** Opposite to direction of velocity. ## Uniform and Non Uniform Motion | Differentiating Parameters | Uniform Motion | Non-uniform Motion | | -------------------------- | ----------------------------------------------------------------------------------- | ------------------------------------------------------------------------------------------------------------------- | | Meaning | Equal distance in equal intervals of time. | Unequal distance in equal intervals of time. | | The average speed | Is the same as the actual speed of the object. | Varies from the actual speed of the object. | | Acceleration | Zero acceleration | Non-zero acceleration | | Distance-time graph | Straight-line graph | Curved line graph | | Example | The motion of a truck on the highway with constant speed | A speedy vehicle with an acceleration undergoes non-uniform motion. | ## Graphical Representation of Motions ### Distance-Time Graph For a distance-time graph, time is taken on the x-axis, and distance is taken on the y-axis. All independent quantities are taken along the x-axis and dependent quantities are taken along the y-axis. ### Velocity-Time Graph for uniform motion of a car  So, the distance s moved by the car in time (t2 – t1) can be expressed as: s = AC × CD = [(40 km h−1) × (t2 – t1) h] = 40 (t2– t1) km = area of the rectangle ABDC (shaded in Fig.) ### Velocity-Time Graph for a car moving with uniform accelerations  s = area ABCDE = area of the rectangle ABCD + area of the triangle ADE = AB × BC + 1/2 (AD × DE) ### Velocity-Time Graphs of an object in non-uniformly accelerated motion: <start_of_image> scale>  ## Equations of Motion | Equation for velocity-time relation | Equation for Displacement-time relation | Equation for Displacement-velocity relation | | ------------------------------------ | ---------------------------------------- | -------------------------------------------- | | v = u + at | s = ut + at²/2 | v² = u² + 2as | **IMPORTANT NOTATION:** v = Final Velocity u = Initial Velocity a = Acceleration t = Time s = Displacement ## Free Fall (motion under gravity) Free fall motion under gravity is when an object moves only under the influence of gravity, without any external forces acting upon it. This motion is accelerated, and is known as **acceleration due to gravity**. ## Uniform Circular Motion * the motion of an object along a circular path covering equal distance along the circumference in the same interval of time is known as **uniform circular motion**. **Examples:** * Motion of Moon * Motion of earth * A cyclist on a circular track **Velocity v for a circular path with radius r and time t:** $v = \frac{2r}{t}$ In any uniform circular motion, the speed remains constant, but the direction of the velocity changes. ## TOP 5 Questions 1. Which of the following statements is correct? * Both speed and velocity are the same * Speed is a scalar and velocity is a vector * Speed is a vector and velocity is a scalar * None of these 2. If a body starts from rest, what can be said about the acceleration of the body? * Positively accelerated * Negatively accelerated * Uniformly accelerated * None of the above 3. Which of the following graphs shows that the body is at rest? * Graph - A * Graph - B * Graph - C * Graph - D 4. The area under a velocity-time (v-t) graph represents a physical quantity which has the unit: * m² * **m** * m³ * m/s 5. A farmer moves along a square field of 10m in 40s. What will the farmer's magnitude of displacement be at the end of 2 minutes 20 seconds from his initial position? “Life’s velocity will always change, just make sure you are in the right direction!" - Motion