Interpret stationary object on distance-time graph
Scenario
Aap parking me car khadi kar ke 2 ghante ke liye movie dekhne gaye. Car wahi ki wahi ruki hui hai, lekin waqt toh aage badh raha hai.
Agar iss situation ka graph banayein, toh kya usme point aage badhega ya apni jagah par ruka rahega?
Mental model
Time kabhi rukta nahi (x-axis aage badhti jayegi), par distance change nahi hoga (y-axis same rahegi). Toh line seedhi right side jayegi flat.
Ek stationary object woh hota hai jo rest par ho. Iska matlab uski position (distance from origin) nahi badal rahi. Graph par time (horizontal) continuously badhta hai, par height (vertical distance) fixed rehti hai, jisse ek perfectly horizontal line banti hai.
Explanation
Physics me motion ko easily samajhne ke liye distance-time graphs ka use hota hai. Is graph mein time ko x-axis (horizontal) aur distance ko y-axis (vertical) par rakha jata hai. Jab bhi hum graph read karte hain, humein ye dekhna hota hai ki waqt (time) guzarne ke saath object ki position me kya badlaav aa raha hai.
Imagine karo ek stationary object, yani koi aisi cheez jo bilkul ruki hui hai (at rest). Maan lijiye ek car aapke ghar se 10 meter door khadi hai. 1 second baad woh 10 meter pe hi hai, 2 second baad bhi 10 meter pe hi hai. Jab aap in points ko graph par plot karoge — (1, 10), (2, 10), (3, 10) — aur unhe jodoge, toh ek straight horizontal line banegi jo time axis ke parallel hogi.
Yeh flat horizontal line clearly dikhati hai ki x-axis par aap aage (right side) to badh rahe ho (time pass ho raha hai), lekin y-axis par aap na to upar gaye aur na neeche aaye (distance mein koi change nahi hua). Iska direct mathematical matlab hai ki object ki speed zero hai.
Board exams mein seedhe MCQ aate hain jahan 4 alag graph dekar pucha jata hai 'which graph represents a body at rest?'. Wahan humesha wo graph chunna hai jisme line totally flat aur horizontal ho.
Worked example
Problem: Look at a distance-time graph. The line starts at y=5m and stays at y=5m from t=0s to t=10s. What is the state of the object?
- Time (0 se 10) badh raha hai par y-value (distance) lagatar 5m hai.
- Jab distance nahi badalta toh object rest par hota hai.
Answer: The object is stationary (at rest).
Problem: How would you graphically represent a tree located 20 m away from an observer over a period of 1 hour?
- Tree move nahi karta, iski distance observer se humesha 20m rahegi.
- Graph par yeh ek seedhi horizontal line banegi y=20 par.
Answer: A horizontal line parallel to the x-axis passing through 20m on the y-axis.
Key points
- Horizontal Line: A stationary object is represented by a straight horizontal line on a distance-time graph.
- Parallel to time axis: The line is completely parallel to the x-axis (time axis) because distance remains constant as time passes.
- Zero slope: A flat line has zero slope, which logically means the speed is 0 m/s.
Common mistakes
- Confusing point on origin with rest: Kuch students sochte hain ki body ruki hui hai tabhi jab graph mein bas origin (0,0) par ek dot ho. Time hamesha aage badhta hai, isliye dot ruka nahi reh sakta, woh ek flat line banayega.
- Confusing flat line in velocity-time graph: Distance-time graph me flat line matlab 'Rest'. Par Velocity-time graph me flat line ka matlab 'Uniform Speed' hota hai. Dono cases mix mat karna.
Recall questions
- What does a horizontal line on a distance-time graph signify?
- If an object is at rest, what is the slope of its distance-time graph?
- What is a key takeaway about interpret stationary object on distance time graph?
Questions & answers
What is the nature of the distance-time graphs for uniform and non-uniform motion of an object? (Part 1: What if it is not moving?)
For an object not moving, the distance-time graph is a straight line parallel to the time axis.
Approach: Visualize that time changes but distance value remains constant.
The distance-time graph of a body is a straight line parallel to the time axis. What is its speed?
Zero.
Approach: Parallel to time axis means the distance is not changing with time. Since Speed = change in distance / time, speed is zero.
Continue learning
Previous: Read coordinates from a line graph