Final answer:
When two objects accelerate from rest with the same constant acceleration, they will have the same final velocity, same displacement, and same time of travel. Therefore, all the statements provided in the question are correct.
Step-by-step explanation:
If two objects X and Y accelerate from rest with the same constant acceleration, several aspects of their motion can be compared. Since they both start from rest and accelerate at the same rate, their velocities will increase uniformly over time. This implies that after the same amount of time has passed, they will both have achieved the same velocity, so statement 1) is correct.
When it comes to their displacements, both objects will also cover the same distance in the same time interval if their accelerations are constant and equal, which means that statement 2) is correct. As for the time of travel, since they both begin from rest and have the same acceleration, they will indeed travel for the same amount of time to reach any given velocity or displacement, making statement 3) correct. Therefore, the correct answer to the question would be 4) All of the above.
Constant acceleration is key here; it means that the rate of change of velocity with time is constant for both objects. The equations of motion for objects under constant acceleration describe their position, velocity, and acceleration over time.