Click to access 9704022.pdf

Straight line portion

In solving the DE that we did together, we should be getting the solution

$$ v = f \tau - f \tau \mathrm{e}^{-\frac{t}{\tau}}$$

You check against our hand written working and try try keying that again in Desmos see if you get a graph that ends at ~10.88 at x=10.

Curved portion

The input into wolfram alpha:

Runge-Kutta method, dv/dt = -v/0.892 + sqrt( 12.2^2 - 0.6^2 * v^4 / 31.83^2 ), v(0)=0, from t=0 to 10, stepsize 0.1

For this input, they should give us a graph. If you look under "Stepwise result", the last column shows $v=10.71$ when $t=10$.

You will want to investigate and change the "r" value. I used r=31.83 of the first lane here. Based on our geometry discussions we should find different radius values for other lanes to see the effect of radius on final velocity.