Question

A person has a reasonable chance of surviving an automobile crash if the deceleration is no more than 30g's.

(a) Calculate the magnitude of the force on a 71 kg person accelerating at this rate.
(b) What distance is traveled by the person if she is brought to rest at this rate from 95 km/h?

Answer 1

To calculate the force on a person in an automobile crash, use Newton's second law of motion and the formula F = m * a, where F is the force, m is the mass, and a is the acceleration. To calculate the distance traveled by the person if they are brought to rest at a deceleration rate of 30g's from a certain velocity, use the kinematic equation d = (v_f^2 - v_i^2) / (2 * a), where d is the distance, v_f is the final velocity, v_i is the initial velocity, and a is the acceleration.

Step-by-step explanation:

(a) To calculate the force on a person in an automobile crash, we can use Newton's second law of motion:

1. Convert the deceleration rate from g's to m/s²: 30g's = 30 * 9.8 m/s² = 294 m/s²
2. Calculate the force using the formula F = m * a, where F is the force, m is the mass, and a is the acceleration:
   F = 71 kg * 294 m/s² = 20,874 N

(b) To calculate the distance traveled by the person if they are brought to rest at a deceleration rate of 30g's from 95 km/h, we can use the kinematic equation:

1. Convert the initial velocity from km/h to m/s: 95 km/h = 95 * (1000 m / 3600 s) = 26.39 m/s
2. Calculate the distance using the equation d = (v_f^2 - v_i^2) / (2 * a), where d is the distance, v_f is the final velocity (0 m/s), v_i is the initial velocity, and a is the acceleration:
   d = (0 - (26.39 m/s)^2) / (2 * (-294 m/s²)) = 12.17 m