Roller-Coaster Physics: Momentum and Velocity After a Constant Force

Given: Mass m = 30 metric tons = 30,000 kg; Force F = 50,000 N; Time t = 12 s; Initial velocity u = 0.

1. Acceleration

Newton's second law: a = F/m = 50,000 N / 30,000 kg = 1.67 m/s².

2. Velocity after 12 s

v = u + at = 0 + (1.67 m/s²)(12 s) = 20.0 m/s (≈ 72 km/h).

3. Momentum after 12 s

p = mv = (30,000 kg)(20.0 m/s) = 600,000 kg·m/s.

Note: The original solution incorrectly used 9.81 m/s² as a factor; momentum is simply mass × velocity.