Misconception in velocity vs. speed definition

Steps:

• Recall that velocity is the rate of change of displacement (vector quantity), while speed is the rate of change of distance (scalar).
• Evaluate A: Gradient of v-t graph gives acceleration (a = Δv/Δt).
• Evaluate B: Matches definition (a = dv/dt).
• Evaluate C: Area under v-t graph gives displacement (∫v dt = s).
• Evaluate D: Incorrectly equates velocity to rate of change of distance, which defines speed.

Why D is correct:

• Velocity requires displacement direction; distance ignores direction, per vector definition v = ds/dt where s is displacement.

Why the others are wrong:

• A is correct: Graph slope directly yields a = rise/run = Δv/Δt.
• B is correct: Standard definition a = dv/dt.
• C is correct: Integration ∫v dt equals displacement.

Final answer: D