Chapter 5, Problem 2A

Why is speed classified as a scalar quantity and velocity classified as a vector quantity?

To determine

To explain: The reason for considering speed as scalar quantity and velocity as vector quantity.

Explanation of Solution

Introduction:

Scalar quantities are the quantities which require only magnitude for its complete description. While for vector quantities, magnitude as well as direction are required for its complete description.

As the speed is rate of change of distance with respect to time. Since distance is the scalar quantity. Speed gives the how fast object is moving. More be the distance travelled by particle in a given time, more be the speed as compared to the small distance travelled by the particle in same time.

  $\therefore \text{Speed}\text{=}\frac{\text{Average}\text{Distance}\text{travelled}\text{by}\text{particle}}{\text{Total}\text{Time}\text{require}}$

In case velocity, velocity is the rate of change of displacement with respect to time. Since displacement is vector quantity. Displacement depends on the particles initial position and final position. If direction of displacement is change, the value of velocity changes.

  $\therefore \text{Velocity}\text{=}\frac{\text{Final}\text{displacement - Initial displacement}}{\text{Total}\text{Time}}$

If particle initially move in the positive direction and finally reached the negative direction of displacement, velocity will be negative in this case, which is not the case for speed, because speed is not direction dependent.

Conclusion:

So, description of the speed can only be given by magnitude wise and description of the velocity given by the magnitude as well as direction. Due to this speed is scalar and velocity is vector quantity.