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Which of the following best describes the appearance of a distance-time graph for an object moving at a uniform speed?
A horizontal line parallel to the time axis
A straight line with a constant positive slope
A vertical line parallel to the distance axis
A curved line with a changing slope
A straight line with a constant positive slope
A distance-time graph represents motion by plotting distance covered on the Y-axis against time on the X-axis. For an object moving at a uniform speed, the distance covered is directly proportional to time, resulting in a straight-line graph.
A distance-time graph represents motion by plotting distance covered on the Y-axis against time on the X-axis. For an object moving at a uniform speed, the distance covered is directly proportional to time, resulting in a straight-line graph.
Think of a car cruising on a highway with the cruise control set to exactly 80 km/h; for every hour that passes, the car covers exactly 80 km, creating a steady, linear progression on a graph.
v=tsтАЛ тАФ defines uniform speed
s=vt тАФ linear equation of motion (y=mx form)
Uniform speed implies that the rate of change of distance with respect to time remains constant. Mathematically, this is expressed as v=╬Фt╬ФsтАЛ. Since the slope of a distance-time graph is equal to the speed, a constant speed yields a constant slope, which geometrically defines a straight line.
The slope of the distance-time graph represents the speed of the object.
A straight line indicates constant velocity (magnitude and direction).
If the line is horizontal, speed is zero (object at rest).
Allows easy calculation of speed from the slope.
Provides a clear visual representation of motion regularity.
Cannot represent instantaneous changes in direction if only speed is plotted.
Kinematic analysis of moving vehicles.
Laboratory experiments involving constant velocity motion (e.g., ticker timer experiments).
Uniform motion is a condition where equal distances are covered in equal intervals of time.
Option A represents an object at rest. Option C is physically impossible as it implies infinite speed at a single instant. Option D represents non-uniform (accelerated) motion.
B is correct тАФ A straight line with a constant positive slope represents uniform speed because the rate of change of distance is constant.
Always check the axes; remember that in a distance-time graph, the steepness (slope) directly correlates to speedтАФsteeper lines mean higher speeds.
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