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Two bodies A and B are travelling in uniform motion, the slope of the distance- time graph of body A is greater than the slope of the distance - time graph of body B. Which of the following statements is correct?
The speed of body A is equal to the speed of body B.
The speed of body A is greater than speed of body B.
The speed of body A is less than the speed of body B.
The acceleration of body A is greater than the acceleration of body B.
The speed of body A is greater than speed of body B.
In a distance-time graph, the speed of an object is represented by the slope of the line. Since the slope of body A is greater than that of body B, body A covers more distance in the same amount of time, indicating a higher speed.
In a distance-time graph, the speed of an object is represented by the slope of the line. Since the slope of body A is greater than that of body B, body A covers more distance in the same amount of time, indicating a higher speed.
Think of a racing track; a runner who covers the track in less time (steeper incline on a graph) is clearly running faster than one who takes a long time.
v=tsтАЛ тАФ Definition of speed as the ratio of total distance covered to total time taken.
tan(╬╕)=horizontal┬аchangevertical┬аchangeтАЛ тАФ The mathematical representation of the slope of a line on a coordinate plane.
For uniform motion, the distance-time graph is a straight line. The slope is defined as the ratio of change in distance (╬Фs) to the change in time (╬Фt). Mathematically, slope = v=╬Фt╬ФsтАЛ. A steeper line indicates a larger value of v.
The slope of a distance-time graph represents the instantaneous or average speed.
A horizontal line on a distance-time graph indicates the object is at rest (speed = 0).
Uniform motion implies constant speed, resulting in a linear graph with a constant slope.
Distance-time graphs provide a clear visual representation of motion parameters.
Cannot represent non-linear or complex path trajectories without specific coordinate systems.
Analyzing vehicle velocity in traffic engineering.
Tracking athletic performance in sports science.
| Feature | Body A | Body B |
|---|---|---|
Relationship to Speed | Higher slope | Lower slope |
Uniform motion means acceleration is zero. Therefore, option D is incorrect because both bodies have zero acceleration.
Option A is incorrect because different slopes imply different rates of motion.
Option C is the inverse of the given condition.
B is correct тАФ The slope of a distance-time graph is directly proportional to the speed of the object.
Always remember: Slope in distance-time graphs = speed; Slope in velocity-time graphs = acceleration.
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