Final answer:
The motor in Rocket A is four times as powerful as the motor in Rocket B because power is the product of force and velocity, and Rocket A has twice the force and achieves twice the velocity in the same time.
Step-by-step explanation:
Regarding the statement on which rocket's motor is more powerful given that Rocket A accelerates twice as quickly as Rocket B, it is necessary to consider the relation between power, force, and acceleration. Power is the rate of doing work or the rate of change of energy, and it can be calculated as the product of force and velocity. In the case of constant acceleration and starting from rest, the final velocity varies directly with acceleration. Since Rocket A accelerates twice as quickly as Rocket B, it will reach a particular point having travelled twice the velocity of Rocket B in the same amount of time.
Assuming a constant mass, the force produced by each engine is proportional to the acceleration (by Newton's second law F = ma). Therefore, if Rocket A is producing twice the acceleration, it is exerting twice the force.
As for power, since it is the product of force and velocity, and Rocket A has twice the force and twice the velocity over the same time interval, its power is 4 times greater than that of Rocket B.
Therefore, the correct statement is: The motor in rocket A is four times as powerful as the motor in rocket B.