Pursuit Problem

To determine the position of the car as a function of time, $x_{car}(t)$, we use the kinematic equation for motion with constant velocity.

The general form for position $x$ at time $t$ is given by: $x(t) = x_0 + v t$ where $x_0$ is the initial position and $v_0$ is the constant velocity.

In this problem, the car passes the police car at time $t=0$. We can define this location as the origin of our coordinate system, so the car's initial position is $x_0 = 0$. The car travels at a constant velocity $v_{car}$. Substituting these values into the equation gives:

$x_{car}(t) = 0 + v_{car} \cdot t$

Therefore, the position equation for the car is:

$x_{car}(t) = v_{car}t$