Interpret uniform velocity on velocity-time graph
Scenario
Agar aap car ko cruise control par `60 km/h` par set kar do, toh agle 1 ghante tak speedometer ki needle `60` se hilegi hi nahi.
Is lagaatar same speed wali needle ko jab graph pe draw karenge, toh wo line kahan ko jayegi?
Mental model
Velocity-Time graph me flat horizontal line matlab 'Speed constant hai' (Cruise control).
Jab `y`-axis par distance na hokar velocity (speed) hoti hai, aur line horizontal ja rahi ho, iska matlab velocity waqt ke sath badal nahi rahi. Ye rest par nahi hai, balki ye bina accelerator dabaye fix speed par bhaag rahi hai.
Explanation
Velocity-time (`v-t`) graph pehle dekhne mein distance-time graph jaisa lagta hai, par iska matlab bilkul alag hota hai. Sabse zaroori baat ye hai ki yahan `y`-axis par velocity (speed) mark ki jati hai. Is graph par hum ye padhte hain ki time (`x`-axis) aage badhne ke sath velocity me kya change aaya hai.
Agar koi object uniform velocity se move kar raha hai, toh iska matlab hai ki uski speed aur direction dono bilkul constant hain. Maan lijiye ek car `20 m/s` ki speed se seedhi road par chal rahi hai bina rukaawat ke. `Time = 1 s` par speed `20`, `time = 5 s` par speed `20`. In points ko jab hum `v-t` graph par plot karke connect karte hain, toh ek perfectly horizontal flat line banti hai jo `x`-axis ke parallel hoti hai.
Yahan bacche sabse badi galti karte hain: distance-time graph mein horizontal line ka matlab 'Rest' hota hai, par `v-t` graph mein horizontal line ka matlab 'Rest' nahi hota. Iska matlab hai object 'constant speed' par move kar raha hai.
Jab object constant speed par hota hai, toh uski speed me koi change nahi aa raha, iska logically matlab ye hai ki uska acceleration `0` hai. Toh ek flat horizontal line in a `v-t` graph indicates uniform velocity and zero acceleration.
Worked example
Problem: A velocity-time graph shows a straight horizontal line at `y = 15 m/s` from `t = 0` to `t = 10 s`. What is the acceleration of the object?
- Line horizontal hai, iska matlab velocity waqt ke sath change nahi ho rahi (`v = u = 15`).
- Acceleration formula: change in velocity / time.
Answer: `0 m/s^2`. The object is moving with uniform velocity.
Problem: How do you represent a body at rest on a velocity-time graph?
- Body at rest ka matlab uski velocity exactly zero hai.
- Velocity `0` hai aur humesha `0` rahegi, to line exactly `x`-axis ke upar banegi.
Answer: A horizontal line lying exactly on the `x`-axis (where `v = 0`).
Key points
- Horizontal Line: On a `v-t` graph, a horizontal line parallel to the time axis indicates uniform (constant) velocity.
- Zero Acceleration: Because the velocity is not changing, the acceleration of the object is `0`.
- Do not confuse with Rest: Unlike a distance-time graph, a flat line here does NOT mean the object is stationary.
Common mistakes
- Interpreting flat line as 'Object at rest': Sabse common trap hai! Exam me dhyan se dekho `y`-axis pe distance likha hai ya velocity. Agar velocity hai, to horizontal line ka matlab constant speed hai, rest nahi.
- Saying acceleration is constant: Technically `0` bhi constant hi hai, par clearly specify karna chahiye ki 'Acceleration is zero'. A constant non-zero acceleration ek teerchi line (slope) banata.
Recall questions
- What does a horizontal line on a velocity-time graph indicate?
- What is the difference between a horizontal line on a distance-time graph and a velocity-time graph?
- What is a key takeaway about interpret uniform velocity on velocity time graph?
Questions & answers
What is the nature of the velocity-time graph for a body moving with uniform velocity?
It is a straight line parallel to the time axis.
Approach: Since velocity is not changing, the y-value remains constant, resulting in a horizontal flat line.
A velocity-time graph is a line parallel to the x-axis. What is the acceleration of the moving body?
Zero.
Approach: Parallel to x-axis means velocity is constant. Acceleration is the rate of change of velocity. If change is 0, acceleration is 0.
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