Apparent weight in a lift

A $58\ \text{kg}$ student stands on a scale in a lift that goes up one floor after another: it speeds up at $1.5\ \text{m/s}^2$ for $2\ \text{s}$, moves steadily for $6\ \text{s}$, then slows at $1.5\ \text{m/s}^2$ for $2\ \text{s}$. You will make the program draw the scale's reading through the trip, and find the lift's top speed from its acceleration.

The idea. The scale reads the push it gives, $N = m(g + a)$, with up positive. The speed is the area under the acceleration graph: in each small step $\Delta t$ it grows by $a\,\Delta t$.

Your tasks.

1. Work out the reading N at every time.
2. Find the largest and smallest readings.
3. Work out the speed at every time, and the top speed.