Question

Which of the following distance-time graphs represents an object in uniform motion?

• A.
• B.
• C.
• D.

Hint:

For distance-time graphs: {Slope = Velocity.} {Horizontal line (slope=0):} Object is at rest (zero velocity). {Straight line with non-zero slope:} Uniform motion (constant velocity). - Positive slope: Moving away from the starting point. - Negative slope: Moving towards the starting point (if distance can be negative or represents position relative to origin). {Curved line:} Non-uniform motion (velocity is changing, i.e., there is acceleration). - Slope increasing (curve gets steeper): Acceleration. - Slope decreasing (curve gets flatter): Deceleration. Always pay attention to the axes labels to correctly interpret the graph.

Answer 1

The Correct Option is B

Concept: Uniform motion means an object travels with a constant velocity. This implies that the object covers equal distances in equal intervals of time. For a distance-time graph:
The slope of the graph represents the velocity of the object.
For uniform motion (constant velocity), the slope must be constant.
A graph with a constant slope is a straight line. Analyzing the Graphs:
Graph (1): This graph shows a curve where the distance covered in successive time intervals is increasing. The slope of the curve is increasing with time. This represents non-uniform motion, specifically accelerated motion (velocity is increasing).
Graph (2): This graph is a straight line passing through the origin with a constant positive slope. A constant slope means constant velocity. This represents uniform motion where the object starts from the origin (distance=0 at time=0) and moves away at a steady speed.
Graph (3): This graph shows a curve where the distance covered in successive time intervals is decreasing (though the total distance is still increasing). The slope of the curve is decreasing with time. This represents non-uniform motion, specifically decelerated motion (velocity is decreasing but still positive, or the rate of increase of distance is slowing down).
Graph (4): This graph is a horizontal straight line. This means that the distance of the object remains constant as time passes. A constant distance implies that the object is not moving; its velocity is zero. An object at rest is technically in uniform motion (zero acceleration), but typically "uniform motion" in such questions implies a constant non-zero velocity. If this were a velocity-time graph, a horizontal line would indicate constant velocity. Conclusion: Graph (2) correctly depicts uniform motion because it is a straight line, indicating a constant rate of change of distance with respect to time (constant velocity). Therefore, the graph representing uniform motion is (2).