Answer :
Final answer:
The acceleration of the roller coaster is 13.4 m/s^2. The force pushing on a 75 kg passenger is 1005 N. The distance required to accelerate the roller coaster is 107.2 m.
Explanation:
a. To find the acceleration of the roller coaster, we can use the equation:
a = (vf - vi) / t
Where vf = final velocity, vi = initial velocity, and t = time. Given that the roller coaster accelerates from 0 to 193 km/hr (53.6 m/s) in 4 seconds, the acceleration can be calculated as:
a = (53.6 - 0) / 4 = 13.4 m/s^2
b. The force pushing on a 75 kg passenger can be calculated using Newton's second law:
F = ma
Where m = mass of the passenger and a = acceleration of the roller coaster. Plugging in the values, we have:
F = 75 kg * 13.4 m/s^2 = 1005 N
c. To find the distance required to accelerate the roller coaster, we can use the equation:
d = (vi * t) + (1/2 * a * t^2)
Where vi = initial velocity, t = time, and a = acceleration. Plugging in the values, we have:
d = (0 * 4) + (1/2 * 13.4 * 4^2) = 107.2 m
