Question

Two identical cars are driving in opposite directions at the same speed. Their kinetic energies have _______________.a. different magnitudes and opposite signsb. different magnitudes, but the same signc. the same magnitude and signd. the same magnitude, but opposite signs

Answer 1

The kinetic energies have the same magnitudes and signs. (c)

Why?

To answer the question, we need to remember the equation to calculate the kinetic energy of a body.

`KE=(1)/(2)*m*v^(2)`

From the equation, we can see that no matter the direction of the movement, if we square the speed, we will get a positive value, so, it means that the kinetic energy will be always positive. Remember, the kinetic energy is not a vector but a scalar value.

Now, from the statement we know that both cars are identical (both have the same mass) and both are moving at the same speed, it means that the kinetic energies for the two cars will have the same magnitude and the same sign.

Have a nice day!

Answer 2

The same magnitude and sign

Step-by-step explanation:

The equation for kinetic energy is
`K=mv^2/2`

Lets assume car's 1 velocity is positive while car's 2 velocity is negative (for example, the first one goes to the right and the second to the left). On both cases when we do
`v^2` the result will be always positive, and since the mass is positive, the kinetic energy is positive. Also, if both cars are identical, they have the same mass, and it is said also that their speed are the same (in magnitude), so this means that their kinetic energies, given by the formula already written, have the same magnitude and sign.