physics-what am i doing wrong?

I think our problem is you are missing the question. It is not how far has the car travelled, it is how mh distance is there from where it started, to where you are taking your measurement. To do that, you have to measure the length of the chord from where it begn, to where 3/4 of the track is circled.

Think of it this way, if he completes the lap, the total displacement is zero

The displacement is a vector pointing from the beginning position to the final position.

So, let's assume your coordinate system is the xy graph from Cartesian geometry.

Then, your starting position is point (50,0) and the ending position is (0,-50).

Draw a triangle (right triangle) with both sides equal to 50. Then the hypotenuse is

h = (50 * 50 + 50 * 50 ) ^ 0.5

= 71

hth.

you have the wrong equation.