Roller Coaster Physics: Distance Traveled in 10 Seconds at Constant Acceleration

Assuming constant acceleration from rest to 128 mph (57.3 m/s) in 5 seconds:

Calculations

• Acceleration: a = v/t = 57.3/5 = 11.46 m/s² (~1.17g)
• Distance in 10 seconds: s = ½at² = 0.5 × 11.46 × 10² = 573 meters (1,880 feet)

Breakdown

• First 5 seconds (acceleration phase): 143 meters (470 ft)
• Next 5 seconds (constant 128 mph): 286 meters (939 ft)
• Total: 429 meters (1,409 ft) at constant speed after acceleration

Reality Check

Actual coasters don't maintain constant acceleration—acceleration peaks early, then tapers. Top speed is often reached before the first hill base. The calculation assumes idealized physics; real tracks include curves, friction, air resistance, and variable grade.

Kingda Ka (128 mph, 3.5s launch) travels ~1,000 ft during launch alone. The 10-second distance would be substantially greater with continued high speed.