Apply average speed formula
Scenario
Aapko ek city dusre city tak jana hai, total rasta `120 km` hai. Agar aap chahte hain ki `2 hours` mein pahunchein, toh aapko lagataar kitni speed maintain karni padegi?
Hum average speed ke formula ko palat (rearrange) kar ke unknown chizein kaise nikalte hain?
Mental model
`v = s / t` ek triangle ki tarah hai. Agar `2` values pata hon, to `3rd` value asani se nikal jati hai.
Formula `v = s / t` (Speed = Distance / Time) mein agar aapko Speed (`v`) aur Time (`t`) diya ho, toh aap inko multiply kar ke Distance (`s`) nikal sakte ho (`s = v * t`). Agar Time nikalna ho, toh `t = s / v` kar sakte ho. Ye ek universal key hai.
Explanation
Pichle topics mein humne padha ki average speed, total distance aur total time ko divide karke aati hai. Equation form mein isko likhte hain:
v = s / t
Yahan `v` (velocity ya speed) ke liye hai, `s` (space ya displacement/distance) ke liye, aur `t` time ke liye hai. (Dhyan rakhna, variables mein `s` distance ke liye use hota hai, speed ke liye nahi).
CBSE exams mein hamesha simple total distance / total time nikalne ko nahi aata. Kai baar woh aapko average speed pehle hi de dete hain aur kisi ek hisse ka distance ya time puchte hain. Aise numericals mein hum formula ko rearrange karte hain. Agar aapko distance nikalna hai, toh aap time ko udhar bhej kar multiply kar denge:
s = v * t
Agar aapko time pata lagana hai, toh formula banega:
t = s / v
Kuch numericals multi-step hote hain. Jaise journey ko `2` parts mein divide kar dete hain (`t_1` aur `t_2`). Aise case mein pehle har part ka time alag se nikalna padta hai (`t_1 = s_1 / v_1`, aur `t_2 = s_2 / v_2`). Phir total time (`t_1 + t_2`) aur total distance (`s_1 + s_2`) ko main formula mein daalna padta hai.
Ek aur zaroori baat: calculation shuru karne se pehle ensure karo ki saari units ek hi system mein hon. Agar distance `km` mein hai, toh speed `km/h` mein honi chahiye, ya time hours mein hona chahiye. Varna conversion zaroori ho jata hai (jaise `5/18` factor use karna).
Worked example
Problem: A car travels at an average speed of `60 km/h` for `2.5 hours`. How much distance did it cover?
- Distance nikalne ke liye speed aur time ko multiply karte hain (`s = v * t`).
- `60` ko `2.5` se multiply karein.
Answer: `150 km`
Problem: A migrating bird flies `120 km` south in `4 hours`, rests for `1 hour`, and then flies another `80 km` in `5 hours`. What is its average speed for the entire trip?
- Total distance ke liye dono hisso ko add karenge.
- Total time nikalte waqt rest wala time bhi count hoga.
- Average speed nikalne ke liye total distance ko total time se divide karenge.
Answer: `20 km/h`
Key points
- The formula triangle: `v = s / t`. Can be rearranged to `s = v * t` (for distance) or `t = s / v` (for time).
- Use correct variables: In physics, `s` usually stands for displacement/distance, not speed. `v` is used for speed/velocity.
- Multi-part journeys: Always find total distance separately and total time separately, then divide them. Do not average the speeds directly.
Common mistakes
- Using 's' for speed: Kai students formula mein speed ki jagah `s` likhte hain. Physics mein `s = distance/displacement`. Speed ko `v` likhna chahiye taaki aage ke equations of motion me confusion na ho.
- Mismatched Units: Distance `km` mein hai aur time seconds mein diya hai. Usme units ko bina match kiye (bina hours me badle) direct divide kar dena result ko completely wrong kar deta hai.
Recall questions
- What formula relates distance (s), speed (v), and time (t)?
- How do you rearrange v = s / t to solve for t?
- What does the symbol 's' represent in kinematics equations?
Questions & answers
A car travels 30 km at a uniform speed of 40 km/h and the next 30 km at a uniform speed of 20 km/h. Find its average speed.
26.67 km/h
Approach: Find t1 = 30/40 = 0.75h. Find t2 = 30/20 = 1.5h. Total time = 2.25h. Total distance = 60 km. Average speed = 60 / 2.25 = 26.67 km/h.
An artificial satellite is moving in a circular orbit of radius 42250 km. Calculate its speed if it takes 24 hours to revolve around the earth.
11065.4 km/h (or 3.07 km/s)
Approach: Distance = Circumference = 2 * pi * r = 2 * 3.14 * 42250 = 265460 km. Speed = Distance / Time = 265460 / 24 = 11060.8 km/h.
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