Question

two rockets with the same mass are accelerated. rocket a accelerates twice as quickly as rocket b. which statement is correct? (1 point) the motor in rocket a is half 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 a third as powerful as the motor in rocket b. the motor in rocket a is four times as powerful as the motor in rocket b.

Explanation:

Step1: Recall Newton's Second Law

Newton's second law states that force \( F = ma \), where \( m \) is mass and \( a \) is acceleration. Since the mass of both rockets is the same (\( m_A = m_B = m \)), the force (which relates to the motor's power here, as more force would mean more power to accelerate) depends on acceleration.

Step2: Define accelerations

Let the acceleration of rocket B be \( a_B = a \). Then the acceleration of rocket A is \( a_A = 2a \) (since it accelerates twice as quickly).

Step3: Calculate forces

For rocket B: \( F_B = m \times a_B = m \times a \)
For rocket A: \( F_A = m \times a_A = m \times 2a = 2ma \)

Step4: Compare forces (power)

Since \( F_A = 2ma \) and \( F_B = ma \), we can see that \( F_A = 2F_B \). So the motor in rocket A is twice as powerful as the motor in rocket B.

Answer:

The motor in rocket A is twice as powerful as the motor in rocket B. (Corresponding to the option: The motor in rocket A is twice as powerful as the motor in rocket B.)