The slope of the straight line displacement-time graph indicates?

1. Analyze the question You're asked what the slope of a straight-line displacement-time graph represents.

2. Explain the concept Slope = change in vertical axis ÷ change in horizontal axis.

For a displacement-time graph:

Slope = Δ(displacement) / Δ(time) = velocity

• A straight line means the slope is constant, so the velocity is constant (uniform velocity).
• A curved line means the slope changes, so the velocity changes (acceleration).

3. Solution, step by step

• Vertical axis: displacement (s)
• Horizontal axis: time (t)
• Slope = (s₂ − s₁)/(t₂ − t₁) = velocity
• Straight line gives a constant slope, which gives uniform velocity.

Checking the options:

• A. Distance traveled: this is read from the vertical axis, not the slope. Wrong.
• B. Uniform velocity: correct.
• C. Uniform acceleration: this would be the slope of a velocity-time graph, or shown by a curved (parabolic) displacement-time graph. Wrong.
• D. Uniform speed: this is close, but speed is a scalar and the graph is of displacement, a vector. Slope of displacement gives velocity, not speed. Wrong.

4. Answer B. uniform velocity.

5. Exam tip Remember the "slope ladder":

• Slope of displacement-time → velocity
• Slope of velocity-time → acceleration
• Area under velocity-time → displacement

Also, watch for the word "displacement" versus "distance" in JAMB questions. Displacement goes with velocity, and distance goes with speed.