Problem: The speed of a bullet is measured to be 640m/s as the bullet emerges from a barrel of length 1.20m. Assuming constant acceleration, find the time that the bullet spends in the barrel after it is fired.

For this problem, we're asked to find the time the bullet remains in the barrel after being fired.

When solving problems with uniformly accelerated motion (UAM), Step Zero is making sure that the acceleration is constant—otherwise, our kinematics equations don’t apply. Then we'll follow these steps to solve the problem:

1. Identify the target, known and unknown variables for each part of the problem —remember that only 3 of the 5 variables (Δx, v₀, v_f, a, and t) are needed to solve any kinematics problem.
2. Choose a UAM equation with only one unknown, which should be our target variable.
3. Solve the equation for the target variable, then substitute known values and calculate the answer.

The four UAM (kinematics) equations are:

$$\begin{gathered} \boxed{\mathbf{ }{\mathit{v}}_{\mathit{f}}\mathbf{ }\mathbf{=}\mathbf{ }{\mathit{v}}_{\mathbf{0}}\mathbf{ }\mathbf{+}\mathit{a}\mathit{t} \\ \mathbf{∆}\mathit{x}\mathbf{=}\mathbf{ }\mathbf{\left(}\frac{{\mathbf{v}}_{\mathbf{f}}\mathbf{+}{\mathbf{v}}_{\mathbf{0}}}{\mathbf{2}}\mathbf{\right)}\mathit{t} \\ \mathbf{∆}\mathit{x}\mathbf{=}\mathbf{ }{\mathit{v}}_{\mathbf{0}}\mathit{t}\mathbf{+}\frac{1}{2}\mathit{a}{\mathit{t}}^{\mathbf{2}} \\ \mathbf{ }{{\mathit{v}}_{\mathit{f}}}^{\mathbf{2}}\mathbf{=}\mathbf{ }{{\mathit{v}}_{\mathbf{0}}}^{\mathbf{2}}\mathbf{ }\mathbf{+}\mathbf{2}\mathit{a}\mathbf{∆}\mathit{x}} \end{gathered}$$