Question 4: Is kinetic energy a vector quantity?

No, Kinetic energy is not a vector quantity. Like any other form of energies, Kinetic Energy is also a scalar quantity. If ‘m’ is the mass of a body and ‘v’ is the speed with which it is moving (magnitude of velocity), its kinetic energy is given by, Here v2 is calculated as the dot product of the velocity vector with itself. Therefore, from mathematics point of view, it is the product of two scalar quantities, m and v2, and must be a scalar.

Physically, it has only magnitude and no direction. An interesting angle to see the problem through is, it is the work done on a body which appears as K.E. As work is a scalar quantity, so is K.E.

Therefore, the quantitative nature of K.E is scalar.

 Why v2 = v.v and not v × v? There might be two arguments that v2 = v.v and not v × v? As a rule of thumb, we look at the value of the product we get. If it needs a direction for its specification, it is a vector product, otherwise a scalar. Now, the same quantity of fuel energy can take a car to east or west or even in a circle. Therefore, we conclude kinetic energy is also a scalar as the fuel energy. – Second, the angle between v and v is zero and hence v × v must be zero as sin0° = 0. But we see the K.E of a body is not zero as the moving body has the ability to do work. Therefore, it must be a dot product.