Question

2. A person with a mass of 50 kg is driving her car at a velocity of 15m / s . The car is involved in a small collision, and the airbag is deployed. The airbag provides a stopping force of 1200 N. The person's final velocity is 0m / s . How long does it take for the person to be stopped by the airbag ?

Answer 1

It takes approximately 0.625 seconds for the person to be stopped by the airbag.

Step-by-step explanation:

We can use the formula for average acceleration to solve this problem:

a = (v_f - v_i) / t

where:

a = average acceleration

v_f = final velocity (0 m/s)

v_i = initial velocity (15 m/s)

t = time

We know that the airbag provides a stopping force of 1200 N, which is equal to the net force on the person-car system. We can use Newton's second law of motion to find the acceleration of the person:

F_net = ma

where:

F_net = net force (1200 N)

m = mass of person (50 kg)

a = acceleration

Solving for a, we get:

a = F_net / m

a = 1200 N / 50 kg

a = 24 m/s^2

Now we can substitute the values of a, v_f, and v_i into the formula for average acceleration and solve for t:

a = (v_f - v_i) / t

24 m/s^2 = (0 m/s - 15 m/s) / t

t = -15 m/s / 24 m/s^2

t = 0.625 s

Therefore, it takes approximately 0.625 seconds for the person to be stopped by the airbag.