A75.0-kg person is riding in a car moving at 20.0 m/s when the car runs into a bridge abutment. (a) calculate the average force on the person if he is stopped by a padded dashboard that compresses an average of 1.00 cm. (b) calculate the average force on the person if he is stopped by an air bag that compresses an average of 15.0 c

The average force on the person if he is stopped by a padded dashboard is -1.5 x 10⁶ N.

The average force on the person if he is stopped by an air bag is -10,000 N.

The given parameters;

The deceleration of the car when the padded dashboard compresses an average of 1.00 cm.

s = 0.01 m

The average force is calculated as;

F = ma

F = 75 x (-20,000)

F = -1.5 x 10⁶ N.

The deceleration of the car when the air bag compresses an average of 15 cm.

s = 0.15 m

The average force is calculated as follows;

F = ma

F = 75 x (-1,333.33)

F = -10,000 N.

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(a)

First of all, we need to calculate the acceleration of the person, by using the following SUVAT equation:

where

v = 0 is the final velocity

u = 20.0 m/s is the initial velocity

a is the acceleration

d = 1.00 cm = 0.01 m is the displacement of the person

Solving for a,

And the average force on the person is given by

with m = 75.0 kg being the mass of the person. Substituting,

where the negative sign means the force is opposite to the direction of motion of the person.

b)

In this case,

v = 0 is the final velocity

u = 20.0 m/s is the initial velocity

a is the acceleration

d  = 15.00 cm = 0.15 m is the displacement of the person with the air bag

So the acceleration is

So the average force on the person is

magnitude and direction

it is called kinetic energy