D) the particle is moving backwards between 10 and 15 seconds

In order for a particle to move backwards, the velocity graph would have to dip below 0. Between 10 and 15 seconds, the particle slows down, but does not go backwards. The particle moves at a constant acceleration with an average velocity of 5 m/s [(10 m/s + 0 m/s)/2] from 0 to 5 seconds, for a displacement of (5 m/s)(5 s) = 25 m. Then from 5 to 10 seconds, it moves at a constant velocity of 10 m/s, so choice C is a true statement; displacement is (10 m/s)(5 s) = 50 m. For the final 5 seconds, it moves with an average velocity of 5 m/s; displacement is 25 m again. Therefore, the total displacement is 25 m + 50 m + 25 m = 100 m, and choice A is true. Choice B is true, a constant slope on the velocity vs. time graph represents constant acceleration.