Question

State which quantity speed is: scalar or vector? Also give an appropriate reason for your stating.

Answer 1

In physics or mathematics, every quantity is classified into only two kinds that is either a vector quantity or a scalar quantity. A scalar quantity is a quantity that has only magnitude or numerical value associated with it. Whereas, a vector quantity is one that has both a numerical value and a direction associated with it. Also remember that speed is the distance travelled by an object in unit time.

Complete answer:
We must remember that the concepts of scalar and vector quantities are concepts brought into Physics, but were originally based in Mathematics. Both scalar and vector quantities have a magnitude associated with it, but vector also has direction associated with it.
So now we know that for a quantity to be scalar it does not need to have direction and for a quantity to be vector it must have direction. Now we must classify to which category of quantities ‘speed’ belongs to; for this let us consider the formula of speed:
$speed = \dfrac{{{\text{distance}}}}{{time}}$
We know that distance is a quantity of measurement, which is equivalent to length.
We also know that time is numerical without a doubt, and does not have direction.
So together, we can say that speed has magnitude but does not have direction, so the correct answer is that speed is a scalar quantity.

Note:
We must be clear that there exists a derivative of speed that has magnitude and direction, it is called velocity.
$velocity = \dfrac{{displacement}}{{time}}$
Here, as we know time is just a magnitude, but displacement is the term that has both magnitude and direction. Displacement is the distance covered by an object with respect to a particular direction. So velocity is the change in the position of an object with respect to direction, in unit time.