Two rockets with the same mass are accelerated. Rocket A accelerates twice as quickly as rocket B. Which statement is correct?(1 point)

To determine the relationship between the power of the motors in the two rockets, we can use the formula for power, which is defined as the product of force and velocity.

Using Newton's second law, force is given by:

\[ F = m \cdot a \]

Where:
- \( F \) is the force,
- \( m \) is the mass of the rocket,
- \( a \) is the acceleration.

Since both rockets have the same mass, we can denote the mass as \( m \) and write the force for each rocket as:
- For Rocket A (with acceleration \( a_A = 2a_B \)):
\[ F_A = m \cdot a_A = m \cdot (2a_B) = 2ma_B \]

- For Rocket B (with acceleration \( a_B \)):
\[ F_B = m \cdot a_B \]

The power \( P \) delivered by each motor can be expressed as:

\[ P = F \cdot v \]

Where \( v \) is the velocity of each rocket. Since Rocket A is accelerating faster than Rocket B, it will reach a higher velocity in a given time, but we also need to consider the time during which it is accelerating.

Power can also be related to the acceleration (considering the same mass) as:

\[ P = F \cdot \text{(average velocity)} \]

If we assume that both rockets start from rest and we are considering the same time period, then the average velocity for Rocket A is higher due to the greater acceleration.

To compare the power:
- Given that Rocket A's acceleration is twice that of Rocket B, the force exerted by Rocket A will be twice that of Rocket B.
- If the average velocity of A is also greater due to the higher acceleration, we can conclude that Rocket A's motor must be more powerful.

When Rocket A accelerates twice as fast, it generates a force that is twice that of Rocket B. Assuming it maintains this acceleration, its power would be related to both the force and the velocity.

Combining these factors intuitively, we find that for Rocket A to have twice the acceleration, and assuming it also translates into a consistent higher output, we can derive that Rocket A's motor must be twice as powerful as Rocket B's motor in order to sustain this higher acceleration over time.

Hence, the correct statement is:

**The motor in rocket A is twice as powerful as the motor in rocket B.**