Jill's Roller Coaster Physics: Zero Average Velocity, Non-Zero Average Speed

Correction to the premise: If Jill returns to her starting point, her displacement is zero, so average velocity = 0. But average speed > 0 (distance traveled / time).

Definitions

• Average velocity = displacement / time = 0 / t = 0 (vector).
• Average speed = total path length / time = positive (scalar).

Example

Track length: 3,000 ft (0.57 mi). Ride time: 2 min (1/30 hr).

• Average speed = 0.57 mi / (1/30 hr) = 17.1 mph.
• Average velocity = 0 mph.

Why It Matters

Velocity captures net effect (nowhere); speed captures effort (thrill). The coaster's engineering delivers high instantaneous speed (70 mph peak) but zero net displacement—a perfect physics metaphor for exhilaration without relocation.