iii. Motion Dynamics: Types, Measurement Method & Spectrum of Movement

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iii. Motion Dynamics: Types, Measurement Method & Spectrum of Movement

Introduction to Movement: Dynamics of Rest and Movement in Everyday Life	Objects can be at rest or in movement in everyday life. Motion is often inferred through indirect evidence, such as the movement of dust indicating air motion. The phenomena of sunrise, sunset, and changing of seasons are related to the motion of the Earth, even if we don’t directly perceive it.
Exploring Straight Lines, Displacement, and the Spectrum of Uniform and Non-Uniform Movements	An object might appear moving to one observer and stationary to another. Example: Trees appear moving to passengers in a bus but stationary to an observer outside. Motions can be complex – straight, circular, rotating, vibrating, or combinations. Location Description: An object’s location is specified using a reference point or origin. Example: A school’s position is described as 2 km north of the railway station, where the railway station serves as the reference point. Motion along a Straight Line: This is the simplest type of motion. If an object starts from point O and moves through points C, B, and A, then the path covered is its distance. Distance: It is the length of the total path covered. E.g., OA + AC = 95 km. It’s a scalar quantity (only magnitude). Displacement: It is defined as the shortest distance from initial to final position. It’s a vector quantity (magnitude + direction). The difference between the final position and the initial position gives displacement. In some cases, displacement can be equal to the distance travelled, like the motion from O to A (60 km). However, displacement might be less than the total distance covered, like in the journey from O to A to B. Displacement can be zero even if distance is not, like if an object returns to its starting point. Uniform Motion and Non-Uniform Motion: Uniform Motion: An object is said to be in uniform motion if it covers equal distances in equal intervals of time. For example, an object moving 5 m every second. Non-Uniform Motion: Objects are said to be in non-uniform motion if they cover unequal distances in equal intervals of time. For example, a car in a crowded street or a person jogging in a park.
Understanding Speed, Velocity, and the Intersection of Distance and Direction	The rate of motion can differ between objects; some may move fast while others move slow. Speed measures the rate of motion i.e., distance traveled in unit time. Speed: Definition: Speed is the distance an object travels in unit time. Units: SI unit: meter per second (m/s). Others: centimetre per second (cm/s), kilometre per hour (km/h). Speed might vary; most objects exhibit non-uniform motion. Average Speed: It is defined as the total distance travelled divided by total time taken. Formula: Average speed = Total distance travelled / Total time taken For example, a car covering 100 km in 2 hours has an average speed of 50 km/h. A speedometer is an instrument on vehicles that shows speed in real-time. An odometer keeps a record of the total distance that the vehicle has travelled. Velocity: Speed with Direction: Velocity is the speed of an object moving in a definite direction. It combines speed and direction. The velocity of an object can be uniform or variable. Average Velocity: For objects with changing velocity at a uniform rate, the average velocity is the mean of the initial and final velocities. Formula: Average velocity = initial velocity + final velocity/ 2 Units: m/s (same as speed).
Exploring Uniform and Non-uniform Motion in Changing Velocities	Uniform vs. Non-uniform Motion: Uniform Motion: An object moves at a constant velocity. There’s no change in velocity over time. Non-uniform Motion: Velocity changes with time, having different values at different moments and points along its path. Acceleration: Definition: Acceleration measures how much the velocity of an object changes in a given time period. Formula: Acceleration = change in velocity/time taken Given the initial velocity u and final velocity v over time t, acceleration a is: a=v-u/t Accelerated Motion: Motion in which there’s a change in velocity over time. Direction: Positive Acceleration: Acceleration is in the direction of velocity. Negative Acceleration (or Deceleration): Acceleration is opposite to the direction of velocity. SI Unit: m s–2 Types of Acceleration: Uniform Acceleration: If an object’s velocity changes by the same amount over equal time intervals. Example: A freely falling body exhibits uniformly accelerated due to gravity. Non-uniform Acceleration: If the rate of change in velocity varies over time. Example: A car that speeds up by different amounts over equal time intervals.

Examples –

Example 1: Usha swims in a 90 m long pool. She covers 180 m in one minute by swimming from one end to the other and back along the same straight path. Find the average speed and average velocity of Usha.

Solution:

The total distance covered by Usha in 1 min is 180 m.

Displacement of Usha in 1 min = 0 m

Average speed = Total distance covered / Total time taken

180m/1min = 180m/ 1min ×1min/60s = 3 m/s

Average velocity = Displacement / Total time taken

= 0m/60 s

= 0 m/s

The average speed of Usha is 3 m/s and her average velocity is 0 m/s.

Example 2: Starting from a stationary position, Rahul paddles his bicycle to attain a velocity of 6 m s–1 in 30 s. Then he applies brakes such that the veMotion and Measurement locity of the bicycle comes down to 4 m s-1 in the next 5 s. Calculate the acceleration of the bicycle in both the cases.

Solution:

In the first case:

initial velocity, u = 0 ; final velocity, v = 6 m s–1 ; time, t = 30 s .

a= v-u/ta

Substituting the given values of u, v and t in the above equation, we get

a= (6ms–1 – 0 ms–1) / 30 s

= 0.2 m s–2

In the second case:

initial velocity, u = 6 m s–1; final velocity, v = 4 m s–1; time, t = 5 s.

Then, a = (4ms–1 –6ms–1) / 5s

= – 0.4 m s–2 .

The acceleration of the bicycle in the first case is 0.2 m s–2 and in the second case, it is – 0.4 m s–2.