Interpret uniform motion on distance-time graph
Scenario
Aap ek cruise control wali gadi mein baithe ho jo lagatar strictly 60 km/h par Highway par chal rahi hai. Har 1 ghante me wo exactly 60 km door pahunch jati hai.
Agar aap pen aur paper lekar har minute uski distance map karo, to graph kaisa dikhega?
Mental model
Uniform motion ek perfect seediyhon (stairs) ki tarah hai. Ek step aage, ek step upar. Graph par yeh ek straight teerchi (sloping) line banti hai.
Jab speed constant hoti hai, toh object equal time interval me exactly equal distance cover karta hai. Graph me jitna waqt (right side) guzar raha hai, usi proportion mein distance (upar) badh raha hai, jisse ek perfectly straight slope wali line milti hai.
Explanation
Uniform motion ka sidha sa matlab hai 'constant speed'. Jab koi object bina speed badhaye ya ghataye lagaatar chalta hai, toh uske motion ko uniform kaha jata hai. Ise distance-time graph par dekhna bohot asaan hai.
Agar ek car har second 10 meter chalti hai (speed 10 m/s), toh pehle second par distance 10m hoga, dusre par 20m, teesre par 30m. Jab hum inhe x aur y axis par mark karke dots ko milaate hain, toh humein ek perfectly straight teerchi (slanted) line milti hai. Yeh line time axis ke respect mein ek angle par uthi hoti hai.
Yeh straight slanting line prove karti hai ki change in distance directly proportional hai change in time ke. Agar ye line curve hone lage — upar ki taraf bend (bend up) ho toh matlab speed badh rahi hai, aur agar neeche ki taraf flat (bend down) hone lage toh speed kam ho rahi hai (non-uniform motion).
Lekin ek baat dhyan rakhein ki ye straight line kahin se bhi shuru ho sakti hai. Agar object exactly starting point se (0 meter) chalna shuru kare, to line Origin (0,0) se niklegi. Par agar object pehle hi aapse 5 meter door khada tha aur fir uniform speed se chala, toh line y-axis par 5m se shuru hokar straight upar jayegi. Dono hi cases uniform motion ke hain.
Worked example
Problem: Examine a distance-time graph showing a straight line passing through (0,0), (1,5), (2,10), and (3,15). What type of motion is this?
- Har 1 second mein distance 5 meter badh raha hai (constant increase).
- Constant speed matlab uniform motion.
Answer: Uniform motion with a constant speed of 5 m/s.
Problem: Which graph represents a car moving on a crowded city road: a straight slanting line or a curved line?
- Crowded road par speed badhti aur ghat-ti rehti hai (brakes lagte hain).
- Non-constant speed curved line (non-uniform motion) banati hai.
Answer: A curved line, as the motion is non-uniform.
Key points
- Straight slanted line: Uniform motion is always represented by a straight line inclined to the time axis on a distance-time graph.
- Equal coverage: It shows that equal distances are covered in equal intervals of time.
- Curves mean non-uniform: If the graph curves upwards or downwards, the speed is changing, meaning the motion is non-uniform.
Common mistakes
- Thinking line must pass through origin: Bache puchte hain ki kya uniform motion ke graph ka zero se shuru hona zaroori hai? Nahi. Starting distance kuch bhi ho sakti hai, bas line perfectly straight honi chahiye.
- Confusing the slope direction: Agar line neeche aane lage (sloping downwards), to wo object wapas starting point ki taraf (return journey) uniform speed se aa raha hai, ye 'negative speed' nahi hai.
Recall questions
- What shape does a distance-time graph take for uniform motion?
- If the distance-time graph is a curved line, what does it indicate?
- What is a key takeaway about interpret uniform motion on distance time graph?
Questions & answers
What is the nature of the distance-time graphs for uniform and non-uniform motion of an object?
For uniform motion, the distance-time graph is a straight line. For non-uniform motion, it is a curved line.
Approach: Differentiate based on the visual shape: straight vs curve.
Draw a distance-time graph for a body moving with a constant speed.
Draw the axes, label x as time, y as distance, and draw a straight line starting from origin (or any y-intercept) sloping upwards.
Approach: Focus on the straight line aspect showing constant proportionality between distance and time.
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