Motion Graphs: Distance vs. Time Slope

In a distance-time graph, the slope represents the speed of the object. For uniform motion, the relationship is:

• Speed = Slope of the distance-time graph
• Mathematically, speed $v = \frac{\Delta d}{\Delta t}$, where $\Delta d$ is the change in distance and $\Delta t$ is the change in time. The slope is calculated as the 'rise' (change in distance) over 'run' (change in time).

Comparing Speeds of Body A and Body B

The problem states that the slope of the distance-time graph for body A is greater than the slope for body B.

• Given: Slope_A > Slope_B

Since the slope directly corresponds to speed in uniform motion, this means:

• Speed_A > Speed_B

Therefore, the speed of body A is greater than the speed of body B.

Analyzing Acceleration

The question specifies uniform motion. In uniform motion, the velocity (and therefore speed) is constant. Constant velocity implies zero acceleration.

• Acceleration = 0 for both body A and body B.
• Option 4, which compares acceleration, is incorrect because acceleration is zero for both objects under uniform motion.

Conclusion

Based on the slope comparison, body A travels faster than body B.

The correct statement is: The speed of body A is greater than speed of body B.