Constant acceleration produces quadratic displacement

Steps:

• Recall that for free fall without air resistance, acceleration g is constant downward.
• Position s = (1/2)gt², so displacement increases quadratically with time.
• At equal time intervals Δt, positions occur at t = 0, Δt, 2Δt, 3Δt, etc.
• Distances between consecutive dots are gtΔt, 3gtΔt, 5gtΔt, etc., increasing linearly.

Why D is correct:

• D shows dots with progressively larger vertical separations, matching the quadratic position formula s = (1/2)gt² under constant acceleration.

Why the others are wrong:

• A: Equal spacing implies constant velocity, ignoring acceleration.
• B: Decreasing spacing suggests deceleration, opposite to gravity.
• C: Irregular or insufficient increase violates quadratic displacement.

Final answer: D