Two rockets with the same mass are accelerated. Rocket A accelerates twice as quickly as rocket B. Which statement is correct?(1 point) Responses The motor in rocket A is equally as powerful as the motor in rocket B. The motor in rocket A is equally as powerful as the motor in rocket B. The motor in rocket A is twice as powerful as the motor in rocket B. The motor in rocket A is twice as powerful as the motor in rocket B. The motor in rocket A is four times as powerful as the motor in rocket B. The motor in rocket A is four times as powerful as the motor in rocket B. The motor in rocket A is half as powerful as the motor in rocket B.

Answer 1

To determine the correct statement about the power of the motors in the two rockets, we need to relate acceleration, force, and power.

The relationship between force, mass, and acceleration is given by Newton's second law:

\[ F = m \cdot a \]

where:

• \( F \) is the force,
• \( m \) is the mass, and
• \( a \) is the acceleration.

According to the problem, Rocket A accelerates twice as quickly as Rocket B. If we let \( a_B \) represent the acceleration of Rocket B, then the acceleration of Rocket A, \( a_A \), is:

\[ a_A = 2a_B \]

Since both rockets have the same mass \( m \), we can express the forces acting on each rocket:

For Rocket B: \[ F_B = m \cdot a_B \]

For Rocket A: \[ F_A = m \cdot a_A = m \cdot (2a_B) = 2m \cdot a_B = 2F_B \]

So, the force exerted by the motor in Rocket A is twice that of Rocket B.

Now, we need to relate force to power. The power \( P \) delivered by a motor is given by:

\[ P = F \cdot v \]

where \( v \) is the velocity of the rocket. For simplicity, we can analyze power in terms of energy required to achieve certain velocities under constant acceleration.

If both rockets are under constant acceleration and start from rest, the work done (which relates to power) will vary with acceleration.

If we assume they are at some moment in time where both rockets have the same velocity, but Rocket A has accelerated to that velocity in less time (due to its greater acceleration), then Rocket A must have exerted a greater average power over that time.

To summarize:

• Since Rocket A accelerates twice as quickly as Rocket B, it is also using a force that is twice that of Rocket B.
• The power is associated with both force and velocity.

However, since Rocket A not only has to exert more force (double) but also is able to reach that velocity quicker (which contributes to it needing more powerful motors), we end up deducing that the motor in Rocket A must indeed be more powerful.

Taking these into account, the power relationship due to acceleration leads to the conclusion that:

The motor in Rocket A is twice as powerful as the motor in Rocket B.

So, the correct statement is:

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