Select correct equation of motion
Scenario
Aapko car ko ek limited jagah me park karna hai. Aapke paas distance pata hai aur speed pata hai, par time nahi pata. Aapke paas 3 alag tool (equations) hain.
Inme se kaunsa tool uthayenge taaki math simple ho aur problem solve ho jaye?
Mental model
Har equation ek chabi (key) ki tarah hai. Check karo ki lock me kaunse variables diye hain aur kya dhoondhna hai, wahi chabi kaam aayegi.
`3` equations (`v = u + at`, `s = ut + 1/2 at^2`, `2as = v^2 - u^2`) me kinematics ke `5` variables (`u`, `v`, `a`, `t`, `s`) khelte hain. Har equation me ek variable bilkul gayab hota hai. Jo variable question me na to diya ho aur na pucha ho, uske hisab se wo equation use karo.
Explanation
Kinematics ke numericals solve karne ka sabse bada secret ye hai ki aap question padh kar sahi equation choose karna seekh jayein. Hamare paas uniformly accelerated motion ki teen (`3`) equations hain:
`v = u + at`
`s = ut + 1/2 at^2`
`2as = v^2 - u^2`
Total paanch (`5`) variables hain: `u` (initial velocity), `v` (final velocity), `a` (acceleration), `t` (time), aur `s` (displacement).
Sahi equation chun-ne ka sabse pehla kadam (step) hai 'Given' aur 'To Find' data likhna. Question padhiye aur saari values likhiye. (Jaise: starts from rest `u = 0`, distance `s = 100`, time `t = 5`. Find acceleration `a`?). Is list ko dekhte hi aapko samajh aa jayega ki is sawal me final velocity (`v`) ka koi zikr nahi hai. Wo na to pata hai, na nikalni hai.
Ab equations ko closely observe karein:
- Pehli equation (`v = u + at`) mein `s` (distance) gayab hai.
- Dusri equation (`s = ut + 1/2 at^2`) mein `v` (final velocity) gayab hai.
- Teesri equation (`2as = v^2 - u^2`) mein `t` (time) bilkul gayab hai.
Kyunki hamare example list me `v` completely missing tha, hum aankh band karke Second Equation lagayenge. Agar question me time (`t`) nahi diya, to seedha Third Equation lagayenge. Agar distance (`s`) ka kaam nahi hai, to First equation. Ye elimination ka rule hamesha kaam karta hai aur calculations me fasne se bachata hai.
Worked example
Problem: A car starts from rest and attains a velocity of `30 m/s` in `10 s`. Which equation should you use to find the acceleration?
- Pehle variables likhein: `u = 0`, `v = 30`, `t = 10`. Pucha kya hai: `a = ?`
- Is list mein konsa variable missing hai? Distance `s`.
- Jis equation me `s` nahi hota, wo first equation hai.
Answer: First equation of motion: `v = u + at`
Problem: A train stops after applying brakes. Its initial velocity was `20 m/s` and retardation is `2 m/s^2`. Which equation should you use to find the stopping distance?
- Variables check karein: stops (`v = 0`), `u = 20`, `a = -2`. Nikaalna hai: distance (`s`).
- Is problem mein kahin bhi time `t` ka zikr nahi hai.
- Jis equation mein `t` nahi aata, wo third equation hai.
Answer: Third equation of motion: `2as = v^2 - u^2`
Key points
- First Equation (v = u + at): Use this when displacement (`s`) is not given and not asked for.
- Second Equation (s = ut + 1/2 at^2): Use this when final velocity (`v`) is not given and not asked for.
- Third Equation (2as = v^2 - u^2): Use this when time (`t`) is completely missing from the problem.
Common mistakes
- Jumping straight to numbers: Bache direct numbers multiply/divide karne lagte hain. Hamesha pehle margins me `u`, `v`, `a`, `t`, `s` list out karo, uske baad equation decide karo.
- Trying to use an equation missing two variables: Agar aapse `s` pucha hai, aur `t` bhi nahi diya gaya, to aap dusri equation (`s = ut + 1/2 at^2`) use nahi kar sakte kyunki ek time par sirf ek hi unknown solve kiya ja sakta hai.
Recall questions
- Which equation of motion does NOT involve displacement (s)?
- Which equation of motion should you use if time (t) is neither given nor asked?
- What is a key takeaway about select correct equation of motion?
Questions & answers
A stone is dropped from a height. Which equation of motion is most suitable to find its final velocity just before touching the ground, given the height and acceleration due to gravity, but not the time of fall?
The third equation of motion: 2as = v^2 - u^2
Approach: Identify the knowns: u (0), a (g), s (height). Identify the unknown: v. The completely missing variable is time (t). The equation without 't' is 2as = v^2 - u^2.
If you need to find the distance covered by a uniformly accelerating car in a given time, and you don't know its final velocity, which equation must you apply?
The second equation: s = ut + 1/2 at^2
Approach: Since final velocity (v) is not known and not asked, use the equation that lacks 'v'.
Continue learning
Previous: Apply acceleration formula
Next: Apply v = u + at
Next: Apply s = ut + 1/2 at^2
Next: Apply 2as = v^2 - u^2