Define average speed
Scenario
Aap Delhi se Agra car se jaate ho. Kahin par speed `100 km/h` hoti hai, kahin traffic ki wajah se `20 km/h`, aur kahin dhaba par rukne se `0`.
Toh agar koi puche ki aap kis speed se gaye, toh aap kya answer doge?
Mental model
`Average speed = Total distance / Total time`. Yeh trip ka ek overall summary nikalta hai.
Jaise marks ka percentage nikalte hain saare subjects ko add karke, waise hi poore raste ka overall idea lene ke liye hum total raste ko total time se divide kar dete hain. Isey farq nahi padta kab fast the kab slow, bas end result batata hai.
Explanation
Real life mein practically kisi bhi vehicle ki speed hamesha constant nahi rehti. Traffic, signals aur turns ki wajah se speed kam ya zyada hoti rehti hai. Aise non-uniform motion ko describe karne ke liye hum 'average speed' ka concept use karte hain.
Average speed nikalna bilkul simple hai: object ne shuru se lekar aakhiri tak total kitna distance cover kiya, aur us pooray safar mein total kitna time laga (jisme dhaba ya signal par rukne ka time bhi shamil hota hai). In dono values ka ratio hi average speed kahlata hai. Formula banta hai: `Average speed = Total distance travelled / Total time taken`.
Iski SI unit `m/s` (meter per second) hoti hai, kyunki hum distance ko meter mein aur time ko second mein naapte hain. Halanki, badi trips ke liye isko `km/h` (kilometer per hour) mein express karna zyada aam hai. Dono units ko ek dusre mein convert karna humne pehle hi sikh liya hai (`5/18` wala rule).
Average speed ek scalar quantity hai, theek distance ki tarah. Yeh hamein direction ke baare mein kuch nahi batati, sirf us particular time frame mein hum kitna fast chal rahe the, uski ek overall picture deti hai. Dhyan rahe, iska matlab yeh nahi hota ki aap har waqt ussi speed par chal rahe the.
Worked example
Problem: An object travels `16 m` in `4 s` and then another `16 m` in `2 s`. What is the average speed of the object?
- Pehle journey ke dono hisson ke distance ko add karke total distance nikalte hain.
- Phir journey mein lage dono times ko add karke total time nikalte hain.
- Average speed ke liye total distance ko total time se divide kar dete hain.
Answer: `5.33 m/s`
Problem: A cheetah chases a prey for `200 m` in `8 s`, gets tired, and jogs the remaining `100 m` in `22 s`. Calculate its average speed.
- Pehle total distance calculate karte hain.
- Phir total time dekhte hain.
- Total distance ko total time se divide kar denge.
Answer: `10 m/s`
Key points
- The formula: `Average speed = Total distance travelled / Total time taken`.
- Includes all time: The 'total time' in the denominator must include any time spent stopping or resting during the journey.
- Scalar Quantity: Like distance, average speed has no direction and is a scalar quantity.
Common mistakes
- Averaging the speeds directly: Bache aksar do alag speeds (jaise `40 km/h` aur `60 km/h`) ko add karke `2` se divide kar dete hain (`average = 50`). Yeh math galat hai. Hamesha `Total Distance / Total Time` wala formula hi apply karna chahiye.
- Forgetting stop times: Agar koi `1` ghanta rest karta hai trip ke beech mein, toh bache us `1 hour` ko total time mein nahi ginte. 'Total time' ka matlab ghar se nikalne aur manzil tak pahunchne ka pura samay hota hai.
Recall questions
- What is the formula to calculate average speed?
- What is the SI unit of average speed?
- Is average speed a scalar or vector quantity?
Questions & answers
A train travels a distance of 15 km at a uniform speed of 30 km/h; the next 75 km at a uniform speed of 50 km/h. What is its average speed for the entire journey?
45 km/h
Approach: Find time for part 1: t1 = 15/30 = 0.5h. Find time for part 2: t2 = 75/50 = 1.5h. Total time = 2h. Total distance = 90 km. Average speed = 90 / 2 = 45 km/h.
State the meaning of average speed.
Average speed is defined as the total distance traveled by an object divided by the total time taken to cover that distance.
Approach: Directly write the definition reflecting the formula 'Total distance / Total time'.
Continue learning
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