MOTION

Motion ka matlab hai position mein change time ke saath. Koi object motion mein hai ya rest par, yeh dekhne ke liye humein ek reference point ya origin ki zaroorat hoti hai.

• Reference Point/Origin: Yeh woh fixed point hota hai jiske respect mein hum kisi object ki position describe karte hain. Jaise, 'school railway station se 2 km North mein hai', yahan railway station reference point hai.
• Relative Motion: Motion hamesha relative hoti hai. Ek object ek observer ke liye rest par ho sakta hai, aur doosre ke liye motion mein. Jaise, train ke andar baithe passengers ek-doosre ke liye rest par hain, par platform par khade aadmi ke liye motion mein hain.

Motion ko describe karne ke liye, reference point ka choose karna bahut important hai.

Motion ko quantify karne ke liye do main terms hain: Distance aur Displacement.

• Distance:
• Yeh object dwara actual path length cover kiya gaya hota hai.
• Yeh ek scalar quantity hai (sirf magnitude hota hai, direction nahi).
• Hamesha positive hota hai ya zero, kabhi negative nahi hota.
• SI unit: metre (m).

• Displacement:
• Yeh object ki initial position se final position tak ki shortest straight line distance hoti hai.
• Yeh ek vector quantity hai (magnitude aur direction dono hote hain).
• Positive, negative ya zero ho sakta hai.
• SI unit: metre (m).

Distance aur Displacement mein Antar (Difference)

| Feature | Distance | Displacement | |:---------------|:---------------------------------------|:-----------------------------------------------| | Definition | Actual path length covered | Shortest distance between initial and final position | | Type | Scalar quantity (only magnitude) | Vector quantity (magnitude + direction) | | Value | Hamesha positive ya zero | Positive, negative ya zero ho sakta hai | | Path | Path par depend karta hai | Path par depend nahi karta, sirf initial aur final position par | | Magnitude | Displacement ke magnitude se ya toh equal ya greater hota hai | Distance ke magnitude se ya toh equal ya less hota hai | | Zero | Kabhi zero nahi hota agar motion hui hai | Zero ho sakta hai agar final position initial position par wapas aa jaye |

Example: Ek circular track par ek round complete karne par:

• Distance: Circumference of the circle (\(2\pi r\))
• Displacement: Zero (kyunki initial aur final position same hai).

Motion ko time ke saath distance cover karne ke pattern ke basis par do types mein classify kiya ja sakta hai:

• Uniform Motion:
• Jab koi object equal intervals of time mein equal distances cover karta hai.
• Ismein object ki speed constant rehti hai.
• Motion ek straight line mein hoti hai.
• Example: Ek car jo highway par constant speed se chal rahi hai.
• Distance-Time graph: Straight line (slope constant).

• Non-Uniform Motion:
• Jab koi object equal intervals of time mein unequal distances cover karta hai.
• Ismein object ki speed variable hoti hai (change hoti rehti hai).
• Example: Ek car jo crowded street par chal rahi hai, ya ek ball jo upar fenki gayi hai.
• Distance-Time graph: Curved line.

Types of Non-Uniform Motion:

1. Accelerated Motion: Speed increase hoti hai (e.g., free fall).
2. Decelerated Motion (Retardation): Speed decrease hoti hai (e.g., brakes lagana).

Rate of motion ko describe karne ke liye Speed aur Velocity ka use hota hai.

• Speed:
• Distance covered per unit time.
• Formula: \( \text{Speed} = \frac{\text{Distance}}{\text{Time}} \)
• Scalar quantity (sirf magnitude).
• SI unit: metre per second (m/s) ya \(m s^{-1}\).
• Other units: km/h, cm/s.
• Average Speed: Total distance travelled divided by total time taken.

\( \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} \)

• Velocity:
• Displacement per unit time.
• Formula: \( \text{Velocity} = \frac{\text{Displacement}}{\text{Time}} \)
• Vector quantity (magnitude aur direction dono).
• SI unit: metre per second (m/s) ya \(m s^{-1}\).
• Velocity change ho sakti hai agar speed change ho, direction change ho, ya dono change ho.
• Average Velocity:
• Agar velocity uniform rate se change ho rahi hai, toh:

\( \text{Average Velocity} = \frac{\text{Initial Velocity (u) + Final Velocity (v)}}{2} \)

• Generally: \( \text{Average Velocity} = \frac{\text{Total Displacement}}{\text{Total Time}} \)

Speed aur Velocity mein Antar (Difference)

| Feature | Speed | Velocity | |:---------------|:----------------------------------------|:----------------------------------------------| | Definition | Distance covered per unit time | Displacement per unit time | | Type | Scalar quantity | Vector quantity | | Value | Hamesha positive ya zero | Positive, negative ya zero ho sakta hai | | Change | Sirf magnitude change hone par change hoti hai | Magnitude, direction ya dono change hone par change hoti hai | | Magnitude | Velocity ke magnitude se ya toh equal ya greater hota hai | Speed ke magnitude se ya toh equal ya less hota hai |

Odometer: Yeh device vehicle mein distance measure karta hai.

Jab koi object non-uniform motion mein hota hai, toh uski velocity change hoti hai. Velocity ke change hone ke rate ko Acceleration kehte hain.

• Acceleration (a):
• Rate of change of velocity.
• Formula: \( \text{Acceleration} = \frac{\text{Change in Velocity}}{\text{Time Taken}} \)
• \( a = \frac{v - u}{t} \) (jahan \(u\) initial velocity hai, \(v\) final velocity hai, aur \(t\) time hai).
• Vector quantity (magnitude aur direction).
• SI unit: metre per second squared (m/s²) ya \(m s^{-2}\).

Types of Acceleration:

1. Uniform Acceleration:

• Agar velocity equal time intervals mein equal amount se change hoti hai.
• Example: Free fall mein object ki motion (gravity ke under).
• Velocity-Time graph: Straight line (slope constant).

1. Non-Uniform Acceleration:

• Agar velocity equal time intervals mein unequal amount se change hoti hai.
• Example: Car ki motion crowded road par.
• Velocity-Time graph: Curved line.

• Positive Acceleration: Velocity increase hoti hai (acceleration motion ki direction mein).
• Negative Acceleration (Retardation/Deceleration): Velocity decrease hoti hai (acceleration motion ke opposite direction mein).

Motion ko graphs se represent karna usko samajhne ka ek effective tareeka hai. Do main types ke graphs hain:

1. Distance-Time Graphs (ya Position-Time Graphs)

• X-axis: Time (independent variable)
• Y-axis: Distance/Position (dependent variable)
• Slope of Distance-Time Graph: Speed deta hai (\( \text{Slope} = \frac{\text{Change in Y}}{\text{Change in X}} = \frac{\text{Distance}}{\text{Time}} \))

Different Scenarios:

1. Object at Rest:

• Graph: Time axis ke parallel straight line.
• Explanation: Distance time ke saath change nahi ho rahi hai, matlab object rest par hai.

1. Uniform Speed (Uniform Motion):

• Graph: Origin se pass hone wali straight line (ya positive slope wali straight line).
• Explanation: Object equal time intervals mein equal distances cover kar raha hai, speed constant hai.

1. Non-Uniform Speed (Non-Uniform Motion):

• Graph: Curved line.
• Explanation: Object equal time intervals mein unequal distances cover kar raha hai, speed variable hai.
• Agar curve upward bend ho raha hai (slope increase ho raha hai), toh speed increase ho rahi hai (accelerated motion).
• Agar curve downward bend ho raha hai (slope decrease ho raha hai), toh speed decrease ho rahi hai (decelerated motion).

2. Velocity-Time Graphs

• X-axis: Time (independent variable)
• Y-axis: Velocity (dependent variable)
• Slope of Velocity-Time Graph: Acceleration deta hai (\( \text{Slope} = \frac{\text{Change in Velocity}}{\text{Time}} = \text{Acceleration} \))
• Area under Velocity-Time Graph: Displacement deta hai (\( \text{Area} = \text{Velocity} \times \text{Time} = \text{Displacement} \))

Different Scenarios:

1. Uniform Velocity (Zero Acceleration):

• Graph: Time axis ke parallel straight line.
• Explanation: Velocity time ke saath change nahi ho rahi hai, acceleration zero hai.

1. Uniform Acceleration:

• Graph: Straight line with positive slope.
• Explanation: Velocity equal time intervals mein equal amount se increase ho rahi hai, acceleration constant aur positive hai.

1. Uniform Retardation (Negative Acceleration):

• Graph: Straight line with negative slope.
• Explanation: Velocity equal time intervals mein equal amount se decrease ho rahi hai, acceleration constant aur negative hai.

1. Non-Uniform Acceleration:

• Graph: Curved line.
• Explanation: Velocity unequal amount se change ho rahi hai, acceleration variable hai.

Jab koi object uniform acceleration se straight line mein move karta hai, toh uski motion ko teen equations se describe kiya ja sakta hai. Yeh equations initial velocity (u), final velocity (v), acceleration (a), time (t), aur displacement (s) ke beech relation batati hain.

1. First Equation of Motion: Velocity-Time Relation

• Equation: \( v = u + at \)
• Derivation (Graphical Method):
• Velocity-time graph mein, acceleration slope hota hai.
• \( a = \frac{\text{Change in velocity}}{\text{Time}} = \frac{v - u}{t} \)
• \( at = v - u \)
• \( v = u + at \)

2. Second Equation of Motion: Position-Time Relation

• Equation: \( s = ut + \frac{1}{2}at^2 \)
• Derivation (Graphical Method):
• Velocity-time graph mein, displacement area under the graph hota hai.
• Area under graph = Area of rectangle + Area of triangle
• Area of rectangle \( = \text{length} \times \text{breadth} = u \times t = ut \)
• Area of triangle \( = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times t \times (v-u) \)
• Since \( v-u = at \) (from 1st equation),
• Area of triangle \( = \frac{1}{2} \times t \times at = \frac{1}{2}at^2 \)
• Total Displacement \( s = ut + \frac{1}{2}at^2 \)
• \( s = ut + \frac{1}{2}at^2 \)

3. Third Equation of Motion: Position-Velocity Relation

• Equation: \( 2as = v^2 - u^2 \)
• Derivation (Graphical Method):
• Velocity-time graph mein, displacement area under the graph hota hai.
• Yeh area ek trapezium ka area bhi hai.
• Area of trapezium \( = \frac{1}{2} \times (\text{sum of parallel sides}) \times \text{height} \)
• \( s = \frac{1}{2} \times (u + v) \times t \)
• First equation se, \( t = \frac{v-u}{a} \)
• \( s = \frac{1}{2} \times (u + v) \times \frac{(v-u)}{a} \)
• \( s = \frac{v^2 - u^2}{2a} \)
• \( 2as = v^2 - u^2 \)

Important Points:

• Yeh equations sirf uniform acceleration ke liye valid hain.
• Free fall ke cases mein, \(a = g\) (acceleration due to gravity) use hota hai. (Approx. \(9.8 m/s^2\) ya \(10 m/s^2\)).
• Agar object rest se start kare, \(u=0\).
• Agar object rest par aa jaye, \(v=0\).

Jab koi object constant speed se circular path par move karta hai, toh uski motion ko Uniform Circular Motion kehte hain.

• Speed constant: Circular motion mein object ki speed constant rehti hai.
• Velocity variable: Har point par direction change hone ki wajah se velocity change hoti rehti hai. Iska matlab hai ki circular motion accelerated motion hai.
• Acceleration: Acceleration hamesha centre ki taraf directed hota hai (centripetal acceleration).
• Speed calculation: Ek round complete karne mein distance \(2\pi r\) (circumference) hoti hai aur time \(T\) (time period) hota hai.

\( \text{Speed (v)} = \frac{\text{Distance}}{\text{Time}} = \frac{2\pi r}{T} \) Jahan \(r\) radius hai aur \(T\) time period hai.

Examples:

• Artificial satellite ka earth ke around motion.
• Moon ka earth ke around motion.
• Ek stone ko thread se baandhkar circular path mein ghumana.