The average speed of a nitrogen molecule in air is about 6.70 ✕ 102 m/s, and its mass is about 4.68 ✕ 10-26 kg.

(a) If it takes 3.80 ✕ 10-13 s for a nitrogen molecule to hit a wall and rebound with the same speed but moving in an opposite direction (assumed to be the negative direction), what is the average acceleration of the molecule during this time interval?
(b) What average force does the molecule exert on the wall?

to calculate

To find the average acceleration of the nitrogen molecule, we can use the formula:

Acceleration (a) = Change in velocity (Δv) / Time interval (Δt)

Since the molecule rebounds with the same speed but in the opposite direction, the change in velocity will be twice the initial velocity. So, Δv = 2 * (6.70 ✕ 10^2 m/s).

We are given the time interval Δt = 3.80 ✕ 10^-13 s.

(a) Substituting these values into the formula:

Acceleration (a) = (2 * (6.70 ✕ 10^2 m/s)) / (3.80 ✕ 10^-13 s)
= (1340 ✕ 10^2 m/s) / (3.80 ✕ 10^-13 s)
= 3.53 ✕ 10^15 m/s^2

So, the average acceleration of the molecule during this time interval is 3.53 ✕ 10^15 m/s^2.

(b) To find the average force exerted by the molecule on the wall, we can use Newton's second law of motion:

Force (F) = Mass (m) * Acceleration (a)

Given the mass of the nitrogen molecule m = 4.68 ✕ 10^-26 kg, and the acceleration a = 3.53 ✕ 10^15 m/s^2:

Force (F) = (4.68 ✕ 10^-26 kg) * (3.53 ✕ 10^15 m/s^2)
= 1.65 ✕ 10^-10 N

So, the average force exerted by the nitrogen molecule on the wall is 1.65 ✕ 10^-10 N.

To find the average acceleration of a nitrogen molecule during a given time interval and the average force it exerts on a wall, we can use Newton's second law of motion, which states that the force exerted on an object is equal to its mass multiplied by its acceleration (F = m * a).

(a) To find the average acceleration of the nitrogen molecule during the given time interval, we can divide the change in velocity by the time taken.

Given:
Initial velocity (v₁) = 6.70 ✕ 10² m/s (positive)
Final velocity (v₂) = -6.70 ✕ 10² m/s (negative)
Time taken (t) = 3.80 ✕ 10⁻¹³ s

Change in velocity (Δv) = v₂ - v₁ = (-6.70 ✕ 10² m/s) - (6.70 ✕ 10² m/s) = -2 * (6.70 ✕ 10² m/s)

Now we can calculate the average acceleration (a) using the formula:
a = Δv / t

a = (-2 * (6.70 ✕ 10² m/s)) / (3.80 ✕ 10⁻¹³ s)

Calculate the value to get the average acceleration.

(b) To find the average force exerted by the nitrogen molecule on the wall, we can use Newton's second law of motion, F = m * a, where m is the mass of the nitrogen molecule.

Given:
Mass of the nitrogen molecule (m) = 4.68 ✕ 10⁻²⁶ kg

We have already calculated the average acceleration (a) in part (a). Multiply the mass of the molecule by the average acceleration to obtain the average force (F) exerted on the wall.

F = m * a

Calculate the value to get the average force exerted on the wall.

By following these steps and calculations, you can find the average acceleration and average force exerted by the nitrogen molecule on the wall.