Two athletes run the same time. One runs the first half of the time with an acceleration of X, the second with

Two athletes run the same time. One runs the first half of the time with an acceleration of X, the second with an acceleration of 2X. Another athlete, on the contrary, the first half of the time with an acceleration of 2X, the second with X. Which of them will run the longer distance?

1st athlete

First half of the time: speed v1 = xt, distance s11 = xt2 / 2.

Second half of the time:

distance s12 = v1t + 2xt2 / 2 = xt * t + 2xt2 / 2 = 4xt2 / 2.

The sum of the distances: s1 = s11 + s12 = xt2 / 2 + 4xt2 / 2 = 5xt2 / 2.

2nd athlete

First half of the time: speed v2 = 2xt, distance s21 = 2xt2 / 2.

Second half of the time:

distance s22 = v2t + xt2 / 2 = 2xt * t + xt2 / 2 = 5 xt2 / 2;

The sum of the distances: s2 = s21 + s22 = 2xt2 / 2 + 5xt2 / 2 = 7xt2 / 2.

Answer: The 2nd athlete will run the longer distance (ratio 7: 5).