Distance-time graph shows deceleration to stop

Steps:

• Identify graph shape: distance increases over time but at a decreasing rate, curving concave down toward a maximum.
• Relate to motion: increasing distance means moving forward; decreasing slope indicates slowing velocity.
• Check for halt: graph flattens to zero slope, showing velocity reaches zero.
• Match options: only braking motion fits this decelerating profile.

Why D is correct:

• Braking train has negative acceleration, so velocity decreases linearly to zero; distance-time graph follows $s = ut + \frac{1}{2}at^2$ with negative $$, yielding concave-down curve ending at constant distance.

Why the others are wrong:

• A: Ball's graph rises parabolically then falls back, decreasing distance after peak.
• B: Speeding car has increasing slope (positive acceleration), forming concave-up curve from origin.
• C: Dropped rock accelerates downward, producing concave-up parabolic increase from rest.

Final answer: D