Highway safety engineers want to design roadside barriers that will crumple in the event that a car drives off the road and collides with them, slowing
down the car more gradually. The average person has a mass of 68 kg and
travels on a highway at a velocity of 27 m/s. If the engineers know that the
maximum force that a person can safely withstand is 2180 N, approximately
how much time is required to crumple the barrier to safely slow the person
with this force?

Explanation:

The impulse-momentum theorem states that the impulse on an object () is equal to the change in momentum of that object ().

Set up the following equation:

Solving for change in momentum:

The momentum of an object is equal to , where is the mass of the object and is the velocity of the object. Since the person's final velocity will be zero, their final momentum will also be zero. Therefore, the person's change in momentum is .

Solving for time:

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