Question

State whether speed is a scalar or a vector quantity. Give reason for your choice.

Answer 1

Hint: To solve the given question first we will know the definition of the terms “scalar quantity” and “vector quantity” and then based on the definitions we will distinguish whether speed is a scalar quantity or a vector quantity.

Complete step by step solution:
Scalar quantities: The quantities which only require magnitude and no direction to describe them are known as scalar quantities.
Vector quantities: The quantities which require both magnitude as well as direction to describe them are called vector quantities.
Speed and velocity formula respectively are given as:
$\text{Speed}={\displaystyle \frac{\text{Distance}}{\text{Time}}}$.
and
$\text{Velocity}={\displaystyle \frac{\text{Displacement}}{\text{Time}}}$
We know what distance and displacement are distance is the actual length of the path covered. So when we take a path with a lot of turns and curves, then the total length we cover is called distance.
Displacement is the difference between the initial and the final positions of the path travelled.
Speed is a scalar quantity because it does not need a direction of motion, it only needs magnitude. We can add speeds without considering the direction of motion. 50 km/hr moving east is the same as 50 km/hr when moving west.
But while for velocity 50 km/hr in east and 50 km/hr in west are different, because it focuses on the final and initial positions of the object.
The speedometer of vehicles just shows speed regardless of the direction of motion.

Note:
We should note that when a vector quantity is multiplied with a scalar quantity, the product obtained is a vector with the same direction but increased magnitude. Speed is a scalar quantity whereas velocity is a vector quantity.