When working with a situation like this (i.e. time-varying force), it's best to start with the differential equations \begin{align} \frac{{\rm d}x}{{\rm d}t}&=v \\ \frac{{\rm d}v}{{\rm d}t}&=F/m \end{align} rather than trying to use positions and velocities from kinematics.

The above can be re-witten using a time-stepping technique called leapfrog integration, in which you update positions and velocities at offset intervals: \begin{align} x^{n+1} &= x^n + v^{n+\frac12}\Delta t \\ a^{n+1} &= F(x^{n+1}) \tag{1}\\ v^{n+\frac32}&=v^{n+\frac12} + a^{n+1}\Delta t \end{align} Here, the fractional $n$ can be thought of the "cell wall" value (e.g., $x_{i+\frac12}=\frac12(x_i+x_{i+1})$) but in time instead of space.

Or you can use a modification called verlocity verlet. This turns (1) into a multi-step process: \begin{align} a_1 &= F\left(x^n_i\right)/m \\ x^{n+1} &= x_i^n + \left(v_i^n + \frac{1}{2}\cdot a_1\cdot\Delta t\right)\cdot\Delta t \\ a_2 & =F\left(x^{n+1}\right)/m \\ v^{n+1} &= v_i^n + \frac{1}{2}\left(a_1+a_2\right)\cdot\Delta t \end{align}

Both integration methods are reasonably simple to implement, requiring definitions for forces and some vectors. The latter of the two is more often the algorithm-of-choice due to it's symplectic nature.

Your implementation for the latter of the two algorithms would essentially be

while t < t_end
    a1 = Force(x) / m
    x += (v + 0.5 * a1 * dt) * dt
    a2 = Force (x) / m
    v += 0.5 * (a1 + a2) * dt
    output t, x, v
    t += dt

When working with a situation like this (i.e. time-varying force), it's best to start with the differential equations \begin{align} \frac{{\rm d}x}{{\rm d}t}&=v \\ \frac{{\rm d}v}{{\rm d}t}&=F/m \end{align} rather than trying to use positions and velocities from kinematics.

The above can be re-witten using a time-stepping technique called leapfrog integration, in which you update positions and velocities at offset intervals: \begin{align} x^{n+1} &= x^n + v^{n+\frac12}\Delta t \\ a^{n+1} &= F(x^{n+1}) \tag{1}\\ v^{n+\frac32}&=v^{n+\frac12} + a^{n+1}\Delta t \end{align} Here, the fractional $n$ can be thought of the "cell wall" value (e.g., $x_{i+\frac12}=\frac12(x_i+x_{i+1})$) but in time instead of space.

Or you can use a modification called verlocity verlet. This turns (1) into a multi-step process: \begin{align} a_1 &= F\left(x^n_i\right)/m \\ x^{n+1} &= x_i^n + \left(v_i^n + \frac{1}{2}\cdot a_1\cdot\Delta t\right)\cdot\Delta t \tag{2}\\ a_2 & =F\left(x^{n+1}\right)/m \\ v^{n+1} &= v_i^n + \frac{1}{2}\left(a_1+a_2\right)\cdot\Delta t \end{align}

Both integration methods are reasonably simple to implement, requiring definitions for forces and some vectors. The latter of the two is more often the algorithm-of-choice due to it's symplectic nature.

The implementation for (2) is basically

while t < t_end
    a1 = Force(x) / m
    x += (v + 0.5 * a1 * dt) * dt
    a2 = Force (x) / m
    v += 0.5 * (a1 + a2) * dt
    t += dt
    output t, x, v

where dt is your time-step (ought to be small, 0.005 should suffice for your values).