Question

During a head-on car crash, a passenger in the front seat of the car accelerates from 13.0 m/s to rest in 0.10 seconds. The passenger is holding a 20.9 kg child on her lap. The passenger is wearing a seat belt, but the child is not. What force must the passenger exert on the child to prevent the child from smashing into the dashboard or windshield?

Answer 1

During the incendent the passenger (and the child as well) experienced the following force:

$$F = ma$$

where $m = 20.9kg$ is the mass of the child, and $a$ is her acceleration. By definition, the acceleration is:

$$a = \dfrac{v}{t}$$

where $v = 13m/s$ is her initial speed, and $t = 0.1s$ is the time she comes to rest. The force the the passenger must exert on the child is equal and opposite to the force $F$. Thus, obtain:

$$F = \dfrac{mv}{t}\\ F = \dfrac{20.9\cdot 13}{0.1} = 2717N$$

Answer. 2717 N.