Give an example of a motion where $x > 0$,$v < 0$,and $a > 0$ at a particular instant.

(N/A) Consider a particle moving in one dimension whose position is given by the function $x(t) = x_0 + A e^{-kt}$,where $x_0 > 0$,$A > 0$,and $k > 0$.
$1$. Position: $x(t) = x_0 + A e^{-kt}$. Since $x_0, A, k, t > 0$,the term $A e^{-kt}$ is positive,so $x(t) > 0$.
$2$. Velocity: $v(t) = \frac{dx}{dt} = -Ak e^{-kt}$. Since $A, k, e^{-kt} > 0$,the product $-Ak e^{-kt}$ is negative,so $v(t) < 0$.
$3$. Acceleration: $a(t) = \frac{dv}{dt} = Ak^2 e^{-kt}$. Since $A, k^2, e^{-kt} > 0$,the acceleration $a(t) > 0$.
An example of such motion is a particle moving towards the origin from the positive side of the $x$-axis,slowing down as it approaches a limiting position $x_0$.