What will the distance-time graph look like for an object moving with uniform speed?
- AOption (a)
The graph looks like a sine wave.
- BOption (b)
The graph cannot be drawn.
- COption (c)
The graph is a zig zag line.
- DOption (d)
The graph is a straight line.
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Correct answer
The graph is a straight line.
Why this answer is correct
The correct answer is The graph is a straight line.
Key Points
- For an object moving with uniform speed, the distance traveled is directly proportional to the time taken. This linear relationship ensures that as time increases, the distance increases at a constant rate.
- In a distance-time graph, time is typically plotted on the X-axis (independent variable) and distance is plotted on the Y-axis (dependent variable).
- The slope of a distance-time graph represents the speed of the object. Since the speed is uniform (constant), the slope remains the same at every point on the graph, which mathematically results in a straight line.
- A straight line passing through the origin (0,0) indicates that the object was at the reference starting point at time zero and moved with a constant velocity thereafter. Hence, statement 4 is correct.
- A sine wave graph represents oscillatory or periodic motion, such as a pendulum, where the position varies harmonically over time. Hence, statement 1 is incorrect.
- A zig-zag line represents non-uniform motion where the speed and direction change abruptly and inconsistently. Hence, statement 3 is incorrect.
Additional Information
- Uniform Motion:
- An object is said to be in uniform motion if it covers equal distances in equal intervals of time, no matter how small these time intervals may be.
- In this state, the acceleration of the object is zero because the velocity does not change in magnitude or direction.
- Non-Uniform Motion:
- If an object covers unequal distances in equal intervals of time, it is in non-uniform motion.
- The distance-time graph for non-uniform motion is a curved line, indicating that the speed is changing (accelerating or decelerating).
- Object at Rest:
- When an object is stationary, its distance from the reference point does not change as time passes.
- The distance-time graph for an object at rest is a horizontal straight line parallel to the time-axis (X-axis), where the slope is zero.
- Speed Calculation from Graph:
- To find the speed from a distance-time graph, one can pick any two points (x1, y1) and (x2, y2) on the line and calculate the gradient.
- The formula used is Speed = (Distance2 - Distance1) / (Time2 - Time1). For a straight line, this value will always be constant.
Important Points
- Steepness of the Graph: The steepness or gradient of the straight line indicates the magnitude of speed. A steeper line represents a higher speed, while a flatter line represents a lower speed.
- Physical Constraints: A distance-time graph can never be a vertical line parallel to the Y-axis. This would imply the object is covering distance in zero time, which means it has infinite speed—a physical impossibility in classical mechanics.
- Comparison: By plotting distance-time lines for two different objects on the same graph, one can easily compare their relative speeds by looking at which line is closer to the Y-axis (steeper).
- Units: Standard SI units used in these graphs are meters (m) for distance and seconds (s) for time, making the unit of the slope (speed) m/s.