Two identical cars are driving in opposite directions at the same speed. their kinetic energies have

a. different magnitudes and opposite signs

b. different magnitudes, but the same sign

c. the same magnitude and sign

d. the same magnitude, but opposite signs

The right answer is c.

Explanation:

The kinetic energy is defined as follows:

K = 1/2 mv²

If both cars are identical, this means that they have the same mass.

Also, we are told that the speed is also the same for both cars.

If they are going in opposite directions, their velocities have the same magnitude, but opposite signs.

But even though they have different signs, the square (which is the parameter relevant for kinetic energy calculations), is always positive, as any number, elevated to an even power, is positive.

So, we conclude that both cars have the same kinetic energy, in magnitude and in sign.