We're asked for the **acceleration** and **force** involved in reversing a particle's velocity.

This problem involves __forces in kinematics__ with __horizontal acceleration__.

Whenever we are given such a problem we apply the following steps.

- Draw a
**free body diagram (FBD)***(usually—this problem doesn't really need it, since only one force is acting.)* - Apply
**kinematics equations**and**F****=****ma** - Solve for the target variable

For part 2, we'll need to use the kinematic equations,

$\overline{)\mathbf{}{{\mathit{v}}}_{{\mathit{f}}}{\mathbf{}}{\mathbf{=}}{\mathbf{}}{{\mathit{v}}}_{{\mathbf{0}}}{\mathbf{}}{\mathbf{+}}{\mathit{a}}{\mathit{t}}\phantom{\rule{0ex}{0ex}}{\mathbf{\u2206}}{\mathit{x}}{\mathbf{=}}{\mathbf{}}\mathbf{\left(}\frac{{\mathit{v}}_{\mathit{f}}\mathbf{+}{\mathit{v}}_{\mathbf{0}}}{\mathbf{2}}\mathbf{\right)}{\mathit{t}}\phantom{\rule{0ex}{0ex}}{\mathbf{\u2206}}{\mathit{x}}{\mathbf{=}}{\mathbf{}}{{\mathit{v}}}_{{\mathbf{0}}}{\mathit{t}}{\mathbf{+}}{\frac{1}{2}}{\mathit{a}}{{\mathit{t}}}^{{\mathbf{2}}}\phantom{\rule{0ex}{0ex}}{\mathbf{}}{{{\mathit{v}}}_{{\mathit{f}}}}^{{\mathbf{2}}}{\mathbf{=}}{\mathbf{}}{{{\mathit{v}}}_{{\mathbf{0}}}}^{{\mathbf{2}}}{\mathbf{}}{\mathbf{+}}{\mathbf{2}}{\mathit{a}}{\mathbf{\u2206}}{\mathit{x}}}$

**Step 1: **Draw a free body diagram (FBD)

We'll take a coordinate system where the positive x-axis points to the right.

Therefore, velocity before the collision with the wall is positive and velocity after the collision (rebounce) with the wall is negative.

**Step 2: **Apply **kinematics equations** and **F****=****ma**

The average speed of a nitrogen molecule in air is about 6.70×10^{ }^{2} m/s, and its mass is 4.68×10^{−26} kg.**(a)** If it takes 3.00×10^{−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 average acceleration of the molecule during this time interval?**(b)** What average force does the molecule exert on the wall?

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