Interpret sign of acceleration
Scenario
Aap highway par race de rahe ho toh aap seat mein peeche dab jate ho (speed badhti hai). Jab achanak red light par break maarte ho, toh seatbelt aage kheench leti hai (speed ghatti hai).
Dono cases mein aapki speed badal rahi hai, toh in dono 'jhatko' ko math ki bhasha mein positive aur negative kaise likhte hain?
Mental model
Positive acceleration = Race dena (speed badhna). Negative acceleration = Brake marna (speed ghatna).
Agar car ki velocity time ke sath badh rahi hai, toh final velocity badi hogi, isliye `(v - u)` positive aayega. Agar velocity kam ho rahi hai, toh `(v - u)` negative aayega, jise hum Retardation ya Deceleration kehte hain.
Explanation
Acceleration ek vector quantity hai, jiska matlab isme direction bhi hoti hai. Jab hum straight line motion ki baat karte hain, toh direction ko dikhane ke liye hum simply `+` (positive) aur `-` (negative) signs ka use karte hain. Ek equation mein sign ki choti si galti pura answer palat sakti hai, isliye iska matlab samajhna bahut zaroori hai.
Jab kisi object ki velocity waqt ke saath badh rahi hoti hai, tab final velocity (`v`) uski initial velocity (`u`) se badi hoti hai. Aise mein formula `a = (v - u)/t` ka result positive number aata hai. Isey hum Positive Acceleration kehte hain. Iska matlab hota hai ki object usi disha mein aur tezi se push ho raha hai jis taraf woh pehle se ja raha tha.
Doosri taraf, jab object ki speed kam ho rahi hoti hai (jaise brakes apply karne par), toh final velocity choti hoti hai. Tab `(v - u)` karne par result negative aata hai. Isey Negative Acceleration kehte hain. Iske do aur popular naam hain: 'Retardation' aur 'Deceleration'. Negative sign ka asal matlab ye hai ki acceleration object ke motion ki disha (direction) ke opposite (ulta) kaam kar raha hai (usko rokne ki koshish kar raha hai).
Ek aur tricky situation hoti hai. Agar koi object negative direction (maan lo peeche) mein chal raha hai aur uski speed badh rahi hai, tab bhi acceleration ka sign negative ho sakta hai. Par Class 9 ke maximum numericals ek hi direction (forward) par focus karte hain, isliye simple rule yaad rakhiye: Speed up = Positive `a`, Slow down = Negative `a`.
Worked example
Problem: A train starts from rest and reaches a speed of `20 m/s` in `5 s`. Find its acceleration and interpret its sign.
- Starts from rest matlab `u = 0`, and final velocity `v = 20`.
- Positive change ko divide karein.
Answer: `+4 m/s^2`. Positive sign means the train is speeding up.
Problem: A car moving at `30 m/s` applies brakes and comes to a stop in `10 s`. Find its acceleration.
- Car stop ho gayi matlab final velocity `v = 0`. Initial velocity `u = 30`.
- `0` me se `30` minus karne par negative result aayega.
Answer: `-3 m/s^2`. Negative sign indicates retardation (brakes applied).
Key points
- Positive Acceleration: Occurs when velocity increases. Final velocity is greater than initial velocity.
- Negative Acceleration (Retardation): Occurs when velocity decreases. Final velocity is less than initial velocity, resulting in a negative sign.
- Directional meaning: A negative sign indicates that the acceleration is acting in the opposite direction to the object's motion.
Common mistakes
- Dropping the negative sign: Bache `(v - u)` karte waqt bade number me se chota minus karke hamesha positive answer nikal dete hain. Brakes lagne par answer compulsory negative aana chahiye.
- Saying 'negative retardation': Word 'retardation' ka khud matlab negative acceleration hai. Toh 'retardation is `-5 m/s^2`' kehna galat hai (double negative). Sahi sentence hai 'retardation is `5 m/s^2`' ya 'acceleration is `-5 m/s^2`'.
Recall questions
- What do we call negative acceleration?
- If an object's speed is decreasing, will its acceleration be positive or negative?
- What is a key takeaway about interpret sign of acceleration?
Questions & answers
A bus decreases its speed from 80 km/h to 60 km/h in 5 s. What does the sign of its calculated acceleration indicate?
The acceleration will be negative, indicating that the bus is slowing down (retardation).
Approach: Since final velocity is less than initial velocity, (v-u) is negative. Explain that this represents an opposing force (brakes).
Can acceleration be negative even if the speed is increasing?
Yes, if the object is moving in the negative direction, an increase in its speed means the acceleration is also in the negative direction.
Approach: This is a conceptual trap. Moving 'backwards' faster means velocity is getting more negative, hence acceleration is negative.
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