Problem: A motorcycle is moving at 30 m/s when the rider applies the brakes, giving the motorcycle a constant deceleration. During the 3.0 s interval immediately after braking begins, the speed decreases to 15 m/s. What distance does the motorcycle travel from the instant braking begins until the motorcycle stops?

In this problem, we are required to calculate the distance covered before stopping given the initial velocity, v₀, the final velocity, v_f, and time, t of the deceleration.

This is a Kinematics problem since it mentions time and initial & final velocities for a constant deceleration.

We'll follow the following simple steps!

1. Identify the target variable, knowns, and Unknowns 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.

We need to remember the four kinematic equations in order to solve the problem. These are:

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