Question

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

O the same magnitude, but opposite signs
O the same magnitude and sign
O different magnitudes, but the same sign
O different magnitudes and opposite signs

Answer 1

Their kinetic energies have the same magnitude and sign.

Step-by-step explanation:

Hi there!

Kinetic energy is not a vector, then it has no direction and therefore it does not matter the sense of movement of the car relative to a system of reference. Mathematically it would be also impossible to obtain a negative kinetic energy. The equation of kinetic energy (KE) is the following:

KE = 1/2 · m · v²

where m is the mass of the car (always positive) and v is its speed (not velocity, remember that the speed is the magnitude of the velocity vector, that´s why the kinetic energy is not a vector. I agree that the "v" in the formula is confusing).

So, even if we use a negative speed (that would be wrong), the kinetic energy will be positive because the speed is squared.

Then, if the cars have the same mass and speed, they will have the same kinetic energy, magnitude and sign (positive).