The slope of a linear distance-times graph represents

Analyze the question: You are asked what the slope (gradient) of a straight-line graph of distance against time represents.

Explain the concept:

• Slope = change in vertical axis ÷ change in horizontal axis.
• On a distance-time graph, the vertical axis is distance and the horizontal axis is time.
• So slope = Δdistance / Δtime. This is the definition of speed.

Note the difference between the two kinds of graph:

• Distance-time graph: slope = speed
• Displacement-time graph: slope = velocity
• Velocity-time graph: slope = acceleration; area under it = distance or displacement

Step-by-step solution:

1. The vertical axis is distance, so the slope is distance ÷ time.
2. Distance ÷ time = speed.
3. Distance is a scalar, so the quantity obtained is a scalar too. That rules out velocity (D), which is a vector and would come from a displacement-time graph.
4. Acceleration (A) comes from a velocity-time graph, and displacement (B) is not a slope at all. It is a quantity plotted on an axis.

A straight line means the slope is constant, so the speed is uniform.

Answer: The correct option is C. speed.

Exam tip: Look at the graph's axis labels and divide the vertical quantity by the horizontal one. "Distance" gives speed, "displacement" gives velocity, and "velocity" gives acceleration. WAEC often tests this distinction between distance and displacement, so check which word is used.