Convert km/h to m/s
Scenario
Aap highway par gaadi mein baith kar speedometer dekhte ho toh speed `km/h` mein likhi hoti hai. Par physics ke problems mein humein aksar speed `m/s` mein chahiye hoti hai.
Speed ko ek unit se dusri unit mein fast kaise badlein bina lamba calculation kiye?
Mental model
`km/h` se `m/s` jaane ke liye bas `5/18` se multiply karna hai — yeh ek magic multiplier hai.
Jab bhi aap speed ko convert karte ho, aap basically `1 km` ko `1000 m` aur `1 hour` ko `3600 s` mein badal rahe ho. `1000 / 3600` ko simplify karne par `5/18` milta hai. Yeh fraction yaad rakhna calculations fast kar deta hai.
Explanation
Physics mein motion padhte waqt aapko hamesha units ka dhyan rakhna padta hai. Bahut saare practical scenarios mein, jaise car ya train ki speed, hum values ko `km/h` mein measure karte hain. Par SI unit system mein, hum distance ko `m` mein aur time ko `s` mein measure karte hain. Isliye, kisi bhi formula mein value daalne se pehle usko `m/s` mein convert karna zaroori hota hai.
Agar hum basic se sochein, toh `1 km = 1000 m` aur `1 hour = 60 min = 3600 s` hota hai. Iska matlab `1 km/h` ki speed asal mein `1000 m / 3600 s` hoti hai:
1 km/h = 1000 m / 3600 s
1 km/h = 5/18 m/s
Jab aap `1000` ko `3600` se divide karke simplify karte ho, toh numerator aur denominator ko `200` se cut karne par `5/18` aata hai. Isliye, `1 km/h` exactly `5/18 m/s` ke barabar hota hai.
Yeh ek bohot powerful shortcut hai. Jab bhi aapko koi speed `km/h` mein di gayi ho, usko `m/s` mein convert karne ke liye sidha us value ko `5/18` se multiply kar do. Example ke liye, agar aapko `36 km/h` ko `m/s` mein badalna hai, toh aapko bas `36 × (5/18)` karna hoga. Yahan `18` denominator mein hai jo `36` ko easily `2` se divide kar dega, aur aapko seedha `10 m/s` mil jayega.
Waise hi, agar aapko kabhi ulta karna ho, yaani `m/s` se `km/h` mein aana ho, toh aap iss multiplier ko flip kar sakte ho. Tab aapko `18/5` se multiply karna hoga. Yeh fraction trick aapko exams mein bohot time bachayegi kyunki CBSE mein aksar values (jaise `18`, `36`, `54`, `72`, `90`) aisi di jaati hain jo `18` ke table mein aati hain, jisse calculation ekdum smooth ho jaata hai.
Worked example
Problem: A train is travelling at a speed of `90 km/h`. Convert this speed into `m/s`.
- Given speed ko `5/18` se multiply karke `m/s` mein convert karte hain.
- `90` ko `18` se divide karne par `5` aata hai. Fir `5` ko `5` se multiply karte hain.
Answer: `25 m/s`
Problem: An athlete is running with a speed of `10 m/s`. Express this speed in `km/h`.
- `m/s` se `km/h` mein jaane ke liye multiplier ulta kar dete hain, yaani `18/5` se multiply karte hain.
- `10` ko `5` se divide karne par `2` milta hai. `2` ko `18` se multiply karke final answer nikalte hain.
Answer: `36 km/h`
Key points
- The magic fraction: To convert `km/h` to `m/s`, multiply the given value by `5/18`.
- Reverse conversion: To convert `m/s` to `km/h`, multiply the given value by `18/5`.
Common mistakes
- Using the wrong fraction: Students often get confused between `5/18` and `18/5`. Yaad rakhein ki 'km' ek badi unit hai aur 'm' chhoti unit hai, toh choti value lane ke liye chote fraction (`5/18`, which is `< 1`) se multiply karna hota hai.
- Forgetting to convert before applying formulas: Problem solve karte waqt agar time `s` (seconds) mein diya ho aur speed `km/h` mein, toh units mismatch hone se answer wrong aayega. Hamesha ensure karein ki units consistent ho.
Recall questions
- What fraction is used to convert `km/h` to `m/s`?
- What is `36 km/h` in `m/s`?
- Does multiplying by `5/18` increase or decrease the numerical value?
Questions & answers
Convert the speed of `72 km/h` into `m/s`.
`20 m/s`
Approach: Multiply `72` by `5/18`. `72` divided by `18` is `4`. Multiply `4` by `5` to get `20`.
A car travels at `54 km/h`. What is its speed in SI units?
`15 m/s`
Approach: Multiply `54` by `5/18`. `54 / 18 = 3`. `3 × 5 = 15`.
Continue learning
Next: Apply average speed formula