Define acceleration
Scenario
Aap ek roller coaster par baithe ho. Woh dheere-dheere upar jaata hai, aur achanak se jab niche girta hai toh aapki dhadkan tez ho jati hai kyunki speed ekdum se bohot zyada badh jati hai.
Is 'speed ke badhne ke jhatke' ya raftaar pakadne ko physics ki language mein kya kehte hain?
Mental model
Acceleration is the 'speed of speed'. Yeh batata hai ki velocity kitni jaldi badal rahi hai.
Jaise Velocity ka matlab hota hai 'Position kitni jaldi badli' (`m/s`), waise hi Acceleration ka matlab hota hai 'Velocity khud kitni jaldi badli' (`m/s / s`). Agar car ka accelerator dabate hi car shoo se aage nikal jaye, toh uska acceleration zyada hai.
Explanation
Real life mein practically kisi object ki velocity hamesha constant nahi rehti. Jab aap car start karte ho, uski velocity zero hoti hai, aur accelerator dabaane par woh dheere-dheere `50 km/h` tak pahunchti hai. Is velocity mein badlaav aane ke rate ko hum 'acceleration' kehte hain.
Acceleration ko technically aise define karte hain: 'Rate of change of velocity with time'. Iska basic formula hota hai: `Acceleration = Change in velocity / Time taken`. Agar ek object ki shuruati (initial) velocity `u` thi aur kuch time `t` ke baad uski final velocity `v` ho gayi, toh change `(v - u)` hoga. Isliye mathematical formula banta hai: `a = (v - u) / t`.
Kyunki velocity ek vector quantity hai jisme direction hoti hai, aur acceleration sidha velocity pe depend karta hai, isliye acceleration bhi ek vector quantity hai. Agar velocity sirf ek disha mein badh rahi hai, tab hum speed badhne ko acceleration maante hain. Agar velocity ki direction badal rahi ho (jaise gadi mud rahi ho), tab bhi acceleration hota hai.
Iski SI unit (`m/s^2`) hoti hai (padhte hain: meter per second square). Yeh unit banti hai (`m/s`) ko time (`s`) se divide karne par. Iska asaan matlab ye hai ki har ek second mein, gaadi ki speed kitne `m/s` se badh rahi hai. Jaise, `a = 2 m/s^2` ka matlab hai har second speed `2 m/s` se badhti jayegi.
Worked example
Problem: A car starts from rest and acquires a velocity of `20 m/s` in `10 seconds`. Calculate its acceleration.
- Rest se start hone ka matlab hai shuruati velocity (`u`) zero hai. Final velocity (`v`) `20 m/s` hai.
- Change ko time se divide karein.
Answer: `2 m/s^2`
Problem: A cyclist moving at `5 m/s` increases his speed to `15 m/s` in a time of `5 seconds`. What is his acceleration?
- Pehle velocity ka difference `(v - u)` nikalte hain.
- Phir use diye gaye time (`5s`) se divide kar dete hain.
Answer: `2 m/s^2`
Key points
- Rate of change: Acceleration is defined as the rate of change of velocity with time.
- Formula: `a = (v - u) / t` (where `v` is final velocity, `u` is initial velocity, and `t` is time).
- Unit: The SI unit of acceleration is `m/s^2`.
Common mistakes
- Confusing (v-u) with (u-v): Bache aksar badi value me se choti minus kar dete hain. Formula humesha (`Final - Initial`) hota hai yani `(v - u)`. Agar speed kam ho rahi hai, toh answer naturally negative aayega, jo ki sahi hai.
- Writing wrong units: Exams mein bacche jaldi mein acceleration ki unit bhi `m/s` likh aate hain. Acceleration `m/s^2` (squared) hoti hai.
Recall questions
- What is the formula for acceleration?
- What is the SI unit of acceleration?
- If an object starts from rest, what is its initial velocity (u)?
Questions & answers
A bus decreases its speed from 80 km/h to 60 km/h in 5 s. Find the acceleration of the bus.
-1.11 m/s^2
Approach: Convert to m/s: u = 80 * 5/18 = 22.22 m/s. v = 60 * 5/18 = 16.67 m/s. a = (16.67 - 22.22) / 5 = -5.55 / 5 = -1.11 m/s^2. Note: The negative sign indicates it is slowing down.
When will you say a body is in uniformly accelerated motion?
When an object travels in a straight line and its velocity increases or decreases by equal amounts in equal intervals of time.
Approach: Define acceleration first, then apply the 'equal changes in equal times' condition.
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