Video Transcript
In the table below, the masses of
four boxes are given. If all the boxes have the same
kinetic energy, which of them has the greatest velocity? (A) Box A, (B) box B, (C) box C,
(D) box D.
In this question, we are given four
boxes, and we want to determine which box has the greatest velocity. First, let’s recall the definition
of kinetic energy. The kinetic energy of an object is
the energy that it possesses due to its motion. It is given by the equation half
𝑚𝑣 squared, where 𝑚 is the mass and 𝑣 is the velocity. We want to make velocity the
subject. We can do this by multiplying both
sides of the equation by two, dividing both sides by 𝑚, and taking the square root
of both sides. This leaves us with 𝑣 equals the
square root of two 𝐾𝐸 over 𝑚.
We are told in the question that
all the boxes have the same kinetic energy. So for convenience, we will label
this kinetic energy as 𝐸. Now we will calculate the velocity
of each box. The mass of box A is given as five
kilograms, so the velocity of box A, 𝑣 A, is given by the square root of two 𝐸
over five. The mass of box B is given as 12
kilograms, so the velocity of box B, 𝑣 B, is given by the square root of two 𝐸
over 12, which equals the square root of 𝐸 over six.
The mass of box C is given as 0.25
kilograms. So, the velocity of box C, 𝑣 C, is
given by the square root of two 𝐸 over 0.25, which equals the square root of eight
𝐸. The mass of box D is given as two
kilograms. So, the velocity of box D, 𝑣 D, is
given by the square root of two 𝐸 over two, which equals the square root of 𝐸.
If we now compare the velocities,
we can see that the velocity of box C is the greatest, followed by box D, box A, and
box B. This means that options (A), (B),
and (D) are incorrect. So, the correct answer is option
(C). Box C has the greatest velocity if
all the boxes have the same kinetic energy.
