To determine how the kinetic energies of objects A and B are related, we first need to understand the equation for kinetic energy.
The kinetic energy (KE) of an object is given by the equation: KE = (1/2) * mass * velocity^2
Given that object A has half the mass and twice the velocity of object B, we can use this information to calculate their respective kinetic energies.
Let's assume that the mass of object B is "m" and its velocity is "v". Therefore, the mass of object A is "m/2" and its velocity is "2v".
Now, let's calculate the kinetic energy of object A: KE_A = (1/2) * (m/2) * (2v)^2 = (1/2) * (m/2) * 4v^2 = (1/4) * m * 4v^2 = m * v^2.
So, the kinetic energy of object A is m * v^2.
Now, let's calculate the kinetic energy of object B: KE_B = (1/2) * m * v^2.
So, the kinetic energy of object B is (1/2) * m * v^2.
Comparing the kinetic energies, we can see that KE_A = m * v^2, and KE_B = (1/2) * m * v^2.
Therefore, the kinetic energy of object A is twice that of object B (Option D: The kinetic energy of A is twice that of B).
To summarize the process:
1. Understand the equation for kinetic energy (KE).
2. Take into account the given information about the objects' mass and velocity.
3. Use these values to calculate the kinetic energy for each object.
4. Compare the results to determine the relationship between the kinetic energies.