The average speed of a nitrogen molecule in air is about 686 m/s, and its mass is 4.85×10-26 kg. If it takes 3.78×10-13 s for a nitrogen molecule to hit a wall and rebound with the same speed but moving in the opposite direction, what is the magnitude of the average acceleration of the molecule during this time interval?

To find the average acceleration of the molecule, we can use the equation for average acceleration:

Acceleration (a) = (Change in velocity)/(Change in time)

First, let's determine the change in velocity of the nitrogen molecule.

The molecule hits the wall and rebounds with the same speed but moving in the opposite direction. Therefore, the change in velocity is equal to twice the initial velocity.

Change in velocity = 2 × Initial velocity

Since the initial velocity is 686 m/s, the change in velocity is:

Change in velocity = 2 × 686 m/s = 1372 m/s

Next, let's determine the change in time.

The problem states that it takes 3.78 × 10^-13 s for the molecule to hit the wall and rebound. This is our change in time.

Change in time = 3.78 × 10^-13 s

Now, we can find the average acceleration using the formula:

Acceleration (a) = Change in velocity / Change in time

Acceleration (a) = 1372 m/s / (3.78 × 10^-13 s)

To simplify this, we can convert the division to multiplication by taking the reciprocal of the change in time:

Acceleration (a) = 1372 m/s × (1 / 3.78 × 10^-13 s)

Now, let's calculate the value of the average acceleration.

Acceleration (a) = 1372 m/s × (2.65 × 10^12 s) [rounded to 2 significant figures]

Acceleration (a) = 3.63 × 10^15 m/s^2

Therefore, the magnitude of the average acceleration of the nitrogen molecule during this time interval is approximately 3.63 × 10^15 m/s^2.

To find the magnitude of the average acceleration of the nitrogen molecule during the time interval, we can use the formula for average acceleration:

average acceleration = (change in velocity) / (change in time)

Since the molecule rebounds with the same speed but moving in the opposite direction, the change in velocity is twice the initial velocity. Therefore, the change in velocity is:

change in velocity = 2 × initial velocity

The initial velocity can be calculated using the formula for average speed:

average speed = total displacement / total time

Since the molecule hits the wall and rebounds, its total displacement is 0. Hence, the initial velocity is:

initial velocity = (average speed)

Substituting the given average speed value:

initial velocity = 686 m/s

Now, let's calculate the magnitude of the average acceleration:

average acceleration = (change in velocity) / (change in time)

Since the molecule rebounds in the opposite direction, the change in velocity is negative:

change in velocity = -2 × initial velocity

change in time = 3.78 × 10^-13 s

Substituting the values:

average acceleration = (-2 × 686 m/s) / (3.78 × 10^-13 s)

Now, we can calculate the magnitude of the average acceleration:

average acceleration = - ([2 × 686 m/s] / [3.78 × 10^-13 s])

Simplifying the expression:

average acceleration ≈ -3.62 × 10^12 m/s^2

Therefore, the magnitude of the average acceleration of the nitrogen molecule during this time interval is approximately 3.62 × 10^12 m/s^2.