The area under a velocity-time graph

A trolley starts at $2\ \text{m/s}$ and speeds up steadily at $1.5\ \text{m/s}^2$ for $8\ \text{s}$. How far does it go? You will make the program add up the area under its velocity-time graph in thin strips, and compare that with the equation of motion.

The idea. A strip of width $\Delta t$ has an area of about $v \times \Delta t$, a small displacement. Adding all the strips gives the displacement:

Your tasks.

1. Inside the loop, add the area of each strip, using the velocity at the strip's middle.
2. Work out the displacement from the equation of motion.
3. Work out the final velocity.