A car traveling at 120 strikes a tree. The front end of the car compresses and the driver comes to rest after traveling 0.90 .

What was the magnitude of the average acceleration of the driver during the collision? Express the answer in terms of "'s," where 1.00 = 9.80 .

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To find the magnitude of the average acceleration of the driver during the collision, we can use the formula:

average acceleration = change in velocity / time

First, let's find the change in velocity. The initial velocity of the driver can be assumed to be zero since they were at rest. The final velocity can be calculated using the equation of motion:

final velocity^2 = initial velocity^2 + 2 * acceleration * displacement

Here, the initial velocity is 0, the displacement is 0.90 m, and the acceleration is what we need to find. We rearrange the equation to solve for the final velocity:

final velocity = sqrt(2 * acceleration * displacement)

Now, the change in velocity is:

change in velocity = final velocity - initial velocity
= final velocity - 0
= final velocity

Therefore, the change in velocity is the same as the final velocity.

Now, let's substitute the given values into the equation:

displacement = 0.90 m
acceleration = ?
1.00 m = 9.80 s

We need to express the answer in terms of "g's," where 1.00 g = 9.80 m/s^2. So, we need to convert the acceleration from m/s^2 to g's.

1 g = 9.80 m/s^2
acceleration (in g's) = acceleration (in m/s^2) / (9.80 m/s^2 per g)

Substituting the values into the formula, we get:

acceleration (in g's) = acceleration (in m/s^2) / (9.80 m/s^2 per g)
= (final velocity) / (9.80)

Now, to find the final velocity, we can use the equation we derived earlier:

final velocity = sqrt(2 * acceleration * displacement)

Substituting the known values, we get:

final velocity = sqrt(2 * acceleration * 0.90)
= sqrt(1.8 * acceleration)

Therefore, the average acceleration of the driver during the collision can be calculated as:

average acceleration = (final velocity) / (9.80)
= sqrt(1.8 * acceleration) / (9.80)

So, the magnitude of the average acceleration of the driver during the collision, expressed in terms of g's, is sqrt(1.8 * acceleration) / 9.80.