Question

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?

Answer 1

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

Explanation:

Let the speed at which we run the second lap be
`v_(2)`

Now by definition of average speed we have

`Speed_(avg)=(Distance)/(Time)`

Let the first lap take a time
`t_(1)` and second lap take a time
`t_(2)`

Thus applying the given conditions in the above equation we have

Total distance covered in 2 laps equals 2d

Thus we have

`Speed_(avg)=(2d)/(t_(1)+t_(2))\\\\Speed_(avg)=(2d)/((d)/(v_(1))+(d)/(v_(2)))`

Thus according to the given condition average speed should be
`2v_(1)`

`\Rightarrow 2v_(1)=(2d)/((d)/(v_(1))+(d)/(v_(2)))\\\\=2v_(1)=(2)/((1)/(v_(1))+(1)/(v_(2)))\\\\\Rightarrow v_(2)=\infty`