Final answer:
Under constant acceleration, a particle starting from rest will cover twice the distance in the second interval of time t seconds than it did in the first interval of the same duration.
Step-by-step explanation:
The question concerns the motion of a particle under constant acceleration. If a particle starts from rest and covers a distance x in t seconds, the distance it will cover in the next t seconds can be determined using the kinematic equation x = x0 + v0t + ½at², where x0 is the initial position, v0 is the initial velocity, a is the acceleration, and t is the time.
Since the particle starts from rest, v0 = 0. We can calculate the distance covered in the first t seconds as x1 = ½at². For the next t seconds, the total time would be 2t, and the new distance x2 can be found as x2 = ½a(2t)². Subtracting the first part from the total, we get x2 - x1 = 2x1, meaning the particle will travel twice the distance in the next t seconds compared to the distance covered in the first t seconds.