You run a lap around the track very slow. let's call it v1. now you have to run another lap much faster so that your average velocity for both laps is 2v1 (twice the speed of v1). how fast do you run lap 2?

Given condition is not physically possible. Speed of second lap should be infinite.

Step-by-step explanation:

Let the speed at which we run the second lap be

Now by definition of average speed we have

Let the first lap take a time and second lap take a time

Thus applying the given conditions in the above equation we have

Total distance covered in 2 laps equals 2d

Thus we have

Thus according to the given condition average speed should be