Shrinking the time interval

A toy car's position is $x = 0.5t^3$, in metres. What is its velocity at exactly $t = 2\ \text{s}$? You will make the program find the average velocity over shorter and shorter intervals after $2\ \text{s}$, and watch it close in on the instantaneous velocity.

The idea.

As $\Delta t$ shrinks, $v_{\text{av}}$ comes closer and closer to $v = \dfrac{dx}{dt}$.

Your tasks.

1. Make the function x(t) return the car's position.
2. Inside the loop, work out the average velocity from t0 to t0 + dt.
3. Work out the exact velocity at t0 from calculus.